effect of pile diameter on modulus of sub-grade reaction

STRUCTURAL SYSTEMS

RESEARCH PROJECT

Report No.

SSRP–2001/22

EFFECT OF PILE DIAMETER ON THE MODULUS OF SUB-GRADE REACTION

by

TEERAWUT JUIRNARONGRIT

SCOTT A. ASHFORD

Final Report Submitted to Caltrans under Contract No. 59A0051

May 2005

Department of Structural Engineering University of California, San Diego La Jolla, California 92093-0085

University of California, San Diego

Department of Structural Engineering

Structural Systems Research Project

Report No. SSRR-2001/22

Effect of Pile Diameter on the Modulus of Sub-Grade Reaction

by

Teerawut Juirnarongrit Graduate Student Researcher

Scott A. Ashford

Assistant Professor of Geotechnical Engineering

Final Report Submitted to Caltrans under Contract No. 59A0051

Department of Structural Engineering

University of California, San Diego

La Jolla, California 92093-0085

May 2005

THIS PAGE LEFT BLANK

Technical Report Documentation Page 1. Report No.

SSRP-2001/22

2. Government Accession No.

3. Recipient’s Catalog No.

4. Title and Subtitle

Effect of Pile Diameter on the Modulus of Subgrade Reaction

5. Report Date

December 2001

6. Performing Organization Code

7. Author(s)

Teerawut Juirnarongrit and Scott A. Ashford

8. Performing Organization Report No.

UCSD / SSRP-2001/22

9. Performing Organization Name and Address

Department of Structural Engineering School of Engineering

10. Work Unit No. (TRAIS)

University of California, San Diego La Jolla, California 92093-0085

11. Contract or Grant No.

59A0051 12. Sponsoring Agency Name and Address

California Department of Transportation

13. Type of Report and Period Covered

Final Report -

Engineering Service Center 1801 30th St., West Building MS-9

Sacramento, California 95807

14. Sponsoring Agency Code

15. Supplementary Notes

Prepared in cooperation with the State of California Department of Transportation.

16. Abstract

Integral pile shaft-columns have been increasingly used for bridge foundations in California because of the economical construction of large diameter Cast-In-Drilled-Hole (CIDH) piles. The current design method of piles against lateral loading involves the use of Winkler’s spring concept with the standard nonlinear p-y curves. However, the accuracy of using these p-y curves for large pile diameters is questionable because they were developed based on relatively small pile diameters. This research study focused on an evaluation of the pile diameter effect on p-y curves through analytical and experimental programs. Furthermore, an assessment of inelastic performance of CIDH piles under cyclic loading was conducted. Instrumented CIDH piles with diameters ranging from 0.4 m to 1.2 m were installed in dense weakly cemented sand, and both vibration tests and lateral load tests were carried out. Data from the tests for each pile diameter were used to back-calculate p-y curves. It was found that the pile diameter has insignificant effect on the p-y curves at the displacement level below the ultimate soil resistance. Beyond this range, the ultimate soil resistance increases as the pile diameter increases. Based on the characteristics of back-calculated p-y curves, a methodology to develop p-y curves for weakly cemented sand is proposed. Using the standard p-y curves currently available in the literature underestimates the soil resistance in weakly cemented sand for small diameter piles, but tends to overestimate the soil resistance to large diameter piles. Therefore, the use of these standard p-y curves for large diameter piles in weakly cemented sand should be used with caution. Finally, results from the cyclic lateral pile load tests show that even low to medium levels of transverse reinforcement (0.6%) can provide adequate seismic performance due to the effect of soil confinement retarding the concrete spalling.

17. Key Words

18. Distribution Statement

Unlimited

19. Security Classification (of this report)

Unclassified

20. Security Classification (of this page)

Unclassified

21. No. of Pages

22. Price

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized

iii

DISCLAIMER

The opinions, recommendations and conclusions contained within this report are

solely those of the authors, and do not necessarily reflect the views of the California

Department of Transportation.

iv

ACKNOWLEDGMENTS

The research described in this report was funded by the California Department of

Transportation (CALTRANS) under contract number 59A0051. Special thanks are due

to Anderson Drilling Company, for the donation of their services for installation of CIDH

piles. Their support is gratefully acknowledged.

v

ABSTRACT

Integral pile shaft-columns have been increasingly used for bridge foundations in

California because of the economical construction of large diameter Cast-In-Drilled-Hole

(CIDH) piles. The current design method of piles against lateral loading involves the use

of Winkler’s spring concept with the standard nonlinear p-y curves. However, the

accuracy of using these p-y curves for large pile diameters is questionable because they

were developed based on relatively small pile diameters. This research study focused on

an evaluation of the pile diameter effect on p-y curves through analytical and

experimental programs. Furthermore, an assessment of inelastic performance of CIDH

piles under cyclic loading was conducted.

Instrumented CIDH piles with diameters ranging from 0.4 m to 1.2 m were

installed in dense weakly cemented sand, and both vibration tests and lateral load tests

were carried out. Data from the tests for each pile diameter were used to back-calculate

p-y curves. It was found that the pile diameter has insignificant effect on the p-y curves

at the displacement level below the ultimate soil resistance. Beyond this range, the

ultimate soil resistance increases as the pile diameter increases. Based on the

characteristics of back-calculated p-y curves, a methodology to develop p-y curves for

weakly cemented sand is proposed.

Using the standard p-y curves currently available in the literature underestimates

the soil resistance in weakly cemented sand for small diameter piles, but tends to

overestimate the soil resistance to large diameter piles. Therefore, the use of these

standard p-y curves for large diameter piles in weakly cemented sand should be used with

caution.

vi

Finally, results from the cyclic lateral pile load tests show that even low to

medium levels of transverse reinforcement (0.6%) can provide adequate seismic

performance due to the effect of soil confinement retarding the concrete spalling.

vii

Table of Contents

DISCLAIMER ................................................................................................................... iii

ACKNOWLEDGMENTS ................................................................................................. iv

ABSTRACT........................................................................................................................ v

Table of Contents.............................................................................................................. vii

List of Figures ................................................................................................................... xii

List of Tables .................................................................................................................. xxv

Chapter 1 INTRODUCTION .......................................................................................... 1

1.1 Objectives of Research ....................................................................................... 3

1.2 Organization of Report ....................................................................................... 4

Chapter 2 LITERATURE REVIEW ............................................................................... 7

2.1 Introduction......................................................................................................... 7

2.2 Methods in Predicting Lateral Pile Responses.................................................... 9

2.2.1 Elastic Continuum using Boundary Element Method ................................ 9

2.2.2 Modified Boundary Element Analyses..................................................... 11

2.2.3 Finite Elements for Soil ............................................................................ 12

2.2.4 Winkler Method and the Concept of p-y Curves ...................................... 13

2.2.4.1 Concept of p-y Curves .......................................................................... 16

2.2.4.2 Soft Clay p-y Curves............................................................................. 18

2.2.4.3 Stiff Clay p-y Curves below Water Table............................................. 18

2.2.4.4 Stiff Clay p-y Curves above Water Table ............................................. 19

2.2.4.5 Sand p-y Curves .................................................................................... 19

2.2.4.6 API Sand p-y Curves............................................................................. 20

2.2.4.7 p-y Curves for c-φ Soils ........................................................................ 21

2.2.4.8 Hyperbolic Soil Model.......................................................................... 22

2.2.4.9 Effect of Pile Diameter on p-y Curves.................................................. 23

2.2.4.10 Development of p-y Curves for Layered Soils ................................. 26

2.2.5 Other Methods .......................................................................................... 27

viii

2.2.5.1 Equivalent Cantilever Approach........................................................... 27

2.2.5.2 Strain Wedge Approach........................................................................ 29

2.3 Full-Scale Pile Testing on Single Piles............................................................. 31

2.4 Inelastic Behavior of Concrete Piles................................................................. 34

2.5 Typical Behavior of Cemented Soil.................................................................. 34

Chapter 3 EVALUATION OF PILE DIAMETER EFFECT USING 3-D FINITE

ELEMENT METHOD...................................................................................................... 67

3.1 Description of Finite Element Model ............................................................... 67

3.2 Linear Elastic Soil Model ................................................................................. 68

3.3 Elasto-Plastic Soil Model.................................................................................. 72

3.4 Limitation of 3-D Finite Element Model .......................................................... 74

3.5 Summary ........................................................................................................... 74

Chapter 4 FULL-SCALE TESTING............................................................................. 87

4.1 Site Description................................................................................................. 87

4.2 Description of Test Piles................................................................................... 90

4.2.1 Pile Geometry and Section Reinforcement Details .................................. 90

4.2.2 Instrumentation of Test Piles .................................................................... 92

4.3 Vibration Testing .............................................................................................. 94

4.3.1 Description of Instrumentation ................................................................. 94

4.3.1.1 Accelerometers ..................................................................................... 94

4.3.1.2 Modal Hammer PCB 086 C50.............................................................. 95

4.3.1.3 Mass Shaker .......................................................................................... 95

4.3.1.4 Recording and Data Processing Instruments ........................................ 96

4.3.2 Testing Procedure ..................................................................................... 97

4.3.2.1 Ambient Vibration Test ........................................................................ 97

4.3.2.2 Impact Vibration Test ........................................................................... 97

4.3.2.3 Forced Vibration Test ........................................................................... 98

4.3.3 Testing Program........................................................................................ 98

4.4 Lateral Load Testing ......................................................................................... 98

ix

4.4.1 Test Setup.................................................................................................. 99

4.4.2 Data Acquisition System........................................................................... 99

4.4.3 Testing Program and Testing Procedure................................................. 100

4.4.3.1 Lateral Load Test 1 ............................................................................. 101




4.5 Summary ......................................................................................................... 104

Chapter 5 TEST RESULTS......................................................................................... 141

5.1 Vibration Testing ............................................................................................ 141

5.1.1 Natural Frequency................................................................................... 141

5.1.1.1 Ambient Vibration Test ...................................................................... 141

5.1.1.2 Impact Vibration Test ......................................................................... 142

5.1.1.3 Forced Vibration Test ......................................................................... 143

5.1.2 Damping Ratio ........................................................................................ 145

5.1.2.1 Impact Vibration Test ......................................................................... 145

5.1.2.2 Forced Vibration Test ......................................................................... 145

5.1.3 Mode Shape ............................................................................................ 146

5.2 Lateral Load Testing ....................................................................................... 147

5.2.1 Lateral Load Test No. 1 .......................................................................... 147

5.2.1.1 Load-Displacement Curves................................................................. 147

5.2.1.2 Longitudinal Strain Gauge Data ......................................................... 148

5.2.1.3 Transverse Strain Gauge Data ............................................................ 149

5.2.1.4 Observed Pile Performance................................................................. 149






x








5.2.5 Comparison of Location of Maximum Moment..................................... 153

5.2.6 Observed Inelastic Behavior of CIDH Piles ........................................... 153

5.3 Summary ......................................................................................................... 154

Chapter 6 ANALYSIS OF TEST RESULTS.............................................................. 191

6.1 Pile Diameter Effect on Initial Modulus of Subgrade Reaction ..................... 191

6.1.1 Method of Analysis................................................................................. 192

6.1.2 Results of Analyses................................................................................. 195

6.1.3 Analysis of Damping .............................................................................. 197

6.2 Pile Diameter Effect on p-y Curves ................................................................ 199

6.2.1 Method for Back-Calculating p-y Curves ............................................... 200

6.2.2 Back-Calculated p-y Curves for CIDH Piles .......................................... 203

6.2.2.1 0.4-m p-y Curves................................................................................. 203

6.2.2.2 0.6-m p-y Curves................................................................................. 203

6.2.2.3 0.9-m p-y Curves................................................................................. 204

6.2.2.4 1.2-m p-y Curves................................................................................. 204

6.2.3 Comparison of p-y Curves for Different Pile Diameters ........................ 205

6.3 Proposed Methodology to Construct p-y Curves for Weakly Cemented Sand

207

6.4 Limitation of Proposed p-y Curves for Design............................................... 208

6.5 Effect of External Confinement from Soil on Bending Behavior................... 209

6.6 Commentary on Effect of External Confinement from Soil on Shear Capacity

of CIDH Pile ............................................................................................................... 211

xi

6.7 Summary ......................................................................................................... 213

Chapter 7 IMPLEMENTATION OF EXISTING p-y CURVES FOR WEAKLY

CEMENTED SAND....................................................................................................... 259

7.1 p-y Curves for Sand ........................................................................................ 260

7.2 p-y Curves for c-φ Soil.................................................................................... 264

7.2.1 Cemented Sand p-y Curves (Ismael 1990) ............................................. 264

7.2.2 p-y Curves for Silt (Reese and Van Impe 2001) ..................................... 265

7.2.3 Comparison of Capability of Various p-y Curves................................... 266

7.3 Summary ......................................................................................................... 267

Chapter 8 SUMMARY AND CONCLUSIONS ......................................................... 287

8.1 Summary ......................................................................................................... 287

8.2 Conclusions..................................................................................................... 287

APPENDIX A................................................................................................................. 289

APPENDIX B ................................................................................................................. 300

APPENDIX C ................................................................................................................. 303

REFERENCES ............................................................................................................... 308

xii

List of Figures

Figure 1.1 Integral Pile-Shaft Column and Moment Profile............................................. 2

Figure 2.1 Influence Factors for Determination of Lateral Pile Responses for the Case of

Constant Soil Modulus (after Poulos, 1971)............................................................. 51

Figure 2.2 Implementation of Winkler Spring Concept for Laterally Loaded Pile

Problem..................................................................................................................... 52

Figure 2.3 Definition of p-y Concept with a) Pile at Rest; b) Pile after Load Applied

(after Dunnavant, 1986) ............................................................................................ 52

Figure 2.4 Typical Family of p-y Curves Response to Lateral Loading (after Dunnavant,

1986) ......................................................................................................................... 53

Figure 2.5 Methodology in Developing p-y Curves (Reese and Van Impe, 2001) ........ 53

Figure 2.6 Characteristic Shape of p-y Curve for Soft Clay a) Static Loading; b) Cyclic

Loading (after Matlock, 1970).................................................................................. 54

Figure 2.7 Characteristic Shape of p-y Curve for Stiff Clay below Water Table for a)

Static Loading; b) Cyclic Loading; c) Value of Constant A (after Reese et al., 1975)

................................................................................................................................... 55

Figure 2.8 Characteristic Shape of p-y Curve for Stiff Clay above Water Table for a)

Static Loading; b) Cyclic Loading (Welch and Reese 1972; Reese and Welch, 1975)

................................................................................................................................... 56

Figure 2.9 Characteristic Shapes of p-y Curves for Sand (Reese et al., 1974)............... 57

Figure 2.10 Sand Failure Modes in Laterally Loaded Pile Problem a) Assumed Passive

Wedge Failure; b) Assumed Lateral Flow Failure (after Reese et al., 1974) ........... 57

Figure 2.11 Values of Coefficients Used for Developing p-y Curves for Sand a)

Coefficient A; b) Coefficient B (after Reese et al., 1974) ........................................ 58

Figure 2.12 Charts Used for Developing API Sand p-y Curves (API, 1987) ................. 58

Figure 2.13 Characteristic Shape of p-y Curve for Cemented Sand (after Ismael, 1990)

................................................................................................................................... 59

xiii

Figure 2.14 Characteristic Shape of p-y Curve for c-φ Soil (Reese and Van Impe, 2001)

................................................................................................................................... 59

Figure 2.15 Initial Subgrade Reaction Constant (Reese and Van Impe, 2001) a) Values

of kc, and b) Values of kφ ......................................................................................... 60

Figure 2.16 Hyperbolic Soil Model (after Carter, 1984) ................................................ 60

Figure 2.17 Comparison of Ratio of Predicted to Measured Pile Head Deflections based

on Two Different Concepts on Pile Diameter Effect (After Ling, 1988) ................. 61

Figure 2.18 Influence of Pile Diameters on Dimensions of Bulb Pressure (Terzaghi,

1955) ......................................................................................................................... 61

Figure 2.19 Typical Determination of Equivalent Depths in a Layered Soil Profile

(Georgiadis, 1983) .................................................................................................... 62

Figure 2.20 Concept of Equivalent Cantilever Beam Method (Chai and Hutchinson,

1999) ......................................................................................................................... 63

Figure 2.21 Design Chart for Determining Depth of Fixity (Budek, 1997) ................... 63

Figure 2.22 Concept of Strain Wedge Model for Analyzing Lateral Load Pile Problem

(Ashour and Norris, 1998) ........................................................................................ 64

Figure 2.23 Distribution of Soil-Pile Reaction along Deflected Pile (Ashour and Norris,

1998) ......................................................................................................................... 64

Figure 2.24 Force-Displacement Hysteretic Loops for Pile Shaft Test a) without

External Confinement, b) with External Confinement (Budek, 1997) ..................... 65

Figure 2.25 Typical Stress-Strain Curves for Cemented Sand (After Clough et al.,

1981); a) Strongly Cemented, b) Weakly Cemented, c) Artificially-Cemented (4%

Cement), d) Artificially-Cemented (2% Cement)..................................................... 66

Figure 3.1 Finite Element Mesh for Pile Diameter Effect Study.................................... 76

Figure 3.2 Typical Results of Compression Stress (σx) and Displacement in Soil in

Laterally Loaded Pile Problem ................................................................................. 77

Figure 3.3 Comparison of Pile Head Displacement obtained from 3D FEM and Elastic

Solution..................................................................................................................... 78

xiv

Figure 3.4 Effect of Pile Diameter on Pile Responses (a) Moment , and (b)

Displacement............................................................................................................. 79

Figure 3.5 Normalized Pile Head Displacement against Normalized Pile Diameter ..... 80

Figure 3.6 Comparison of Pile Responses obtained form 3D FEM and LPILE (a)

Moment , and (b) Displacement................................................................................ 81

Figure 3.7 Displacement at Pile Head against Modulus of Subgrade Reaction ............. 82

Figure 3.8 Normalized Pile Head Displacement against Normalized Modulus of

Subgrade Reaction .................................................................................................... 82

Figure 3.9 Comparison of Two Different Concepts on Pile Diameter Effect on Modulus

of Subgrade Reaction with Results from 3D FEM .................................................. 83

Figure 3.10 Effect of Pile Diameter on Lateral Pile Responses (a) Pile Head

Displacement, and (b) Ratio of Maximum Moment to Yield Moment .................... 84

Figure 3.11 Comparison of Moment Profiles for Linear and Nonlinear Analyses......... 85

Figure 3.12 Comparison of Normalized Pile Head Displacement against Normalized

Pile Diameter for Linear and Nonlinear Analyses.................................................... 86

Figure 4.1 Location Map of UCSD East Campus Test Site ..................................... 111

Figure 4.2 Topographic Map of UCSD East Campus Test Site ................................... 112

Figure 4.3 Geologic Map of UCSD East Campus Test Site (Elliot 1988) ................... 113

Figure 4.4 Location Map of Subsurface Exploration.................................................... 114

Figure 4.5 Soil Boring Log for Test Site (Borehole BH-1) .......................................... 115

Figure 4.6 Soil Boring Log for Test Site (Borehole BH-2) .......................................... 118

Figure 4.7 Soil Condition at Test Site Including (a) Corrected SPT-N-Values, and (b)

Shear Wave Velocity Profile .................................................................................. 121

Figure 4.8 Additional Locations of Soil Investigation Extracted from Available Soil

Reports .................................................................................................................... 122

Figure 4.9 Pile Cross Section........................................................................................ 123

Figure 4.10 Steel Stress-Strain Curves for 0.6-m and 0.9-m Piles ............................... 124

Figure 4.11 Steel Stress- Strain Curves for 0.4-m and 1.2-m Piles .............................. 125

Figure 4.12 Sequence of CIDH Pile Installation .......................................................... 126

xv

Figure 4.13 Construction of Reinforcement for Load Stub .......................................... 127

Figure 4.14 Completion of Form Works for Load Stubs.............................................. 127

Figure 4.15 Installation of Tiltmeters into Inclinometer Casing................................... 128

Figure 4.16 Locations of Crossbow Accelerometers for the 0.4-m and 1.2-m CIDH Piles

in Forced Vibration Test ......................................................................................... 129

Figure 4.17 Modal Hammer Used for Impact Vibration Test ...................................... 130

Figure 4.18 Eccentric Mass Shaker .............................................................................. 131

Figure 4.19 Aluminum Buckets with Two Aluminum Plates on Each of Them.......... 131

Figure 4.20 Relationship between Dynamic Force and Excitation Frequency for

Different Masses of Aluminum Buckets................................................................. 132

Figure 4.21 Modal Hammer Striking on Load Stub to Generate Initial Velocity to 0.6-m

CIDH Pile for Impact Vibration Test...................................................................... 133

Figure 4.22 Mass Shaker Mounted on Top of Load Stub of 0.6-m CIDH Pile to

Generate Harmonic Force Excitation to the Pile .................................................... 133

Figure 4.23 Lateral Pile Load Test Sequence ............................................................... 134

Figure 4.24 Lateral Load Test Set-up and Locations of Instruments (Test No.1) ........ 135




Figure 4.28 Test Setup for Lateral Load Test No.1 ...................................................... 139

Figure 4.29 UCSD Data Acquisition System ............................................................... 139

Figure 5.1 Power Spectra for 0.4-m CIDH Pile from Ambient Vibration Tests (E-W

Direction) ................................................................................................................ 159


Direction) ................................................................................................................ 159


Direction) ................................................................................................................ 160

Figure 5.4 Comparison of Power Spectra for Various Pile Diameters from Ambient

Vibration Tests (E-W Direction) ............................................................................ 160

xvi

Figure 5.5 Frequency Response Functions for 0.4-m CIDH Pile from Impact Vibration

Tests (E-W Direction)............................................................................................. 161





Figure 5.8 Frequency Response Functions for 1.2-m CIDH Pile (No.1) from Impact


Figure 5.9 Frequency Response Functions for 1.2-m CIDH Pile (No.2) from Impact


Figure 5.10 Comparison of Frequency Response Functions for Various Pile Diameters

from Impact Vibration Tests (E-W Direction)........................................................ 163

Figure 5.11 Frequency Response Curves for 0.4-m Pile from Forced Vibration Tests 164


Figure 5.13 Frequency Response Curves for 0.6-m Pile from Forced Vibration Tests

(after Pile Experienced Highest Amplitude of Excitation Force)........................... 165



(after Pile Experienced Highest Amplitude of Excitation Force)........................... 166

Figure 5.16 Frequency Response Curves for 1.2-m Pile (No.1) from Forced Vibration

Tests ........................................................................................................................ 166


Tests (after Pile Experienced Highest Amplitude of Excitation Force) ................. 167


Tests ........................................................................................................................ 167


Tests (after Pile Experienced Highest Amplitude of Excitation Force) ................. 168

Figure 5.20 Comparison of Frequency Response Curves for Various Pile Diameters

from Forced Vibration Tests................................................................................... 168

xvii

Figure 5.21 Acceleration vs. Time for CIDH Piles from Impact Vibration Tests (E-W

Direction) ................................................................................................................ 169

Figure 5.22 Comparison of Damping Ratio Obtained from Impact and Forced Vibration

Tests ........................................................................................................................ 170

Figure 5.23 Relationship between Mass of Bucket and Damping Ratio for Various Pile

Diameters ................................................................................................................ 170

Figure 5.24 Mode Shape of Each Pile .......................................................................... 171

Figure 5.25 Static Load-Displacement Curves for 0.6-m and 0.9-m CIDH Piles before

Correction ............................................................................................................... 172

Figure 5.26 Static Load-Displacement Curves of 0.9-m Pile Obtained from Phase I and

Phase II.................................................................................................................... 172

Figure 5.27 Static Load-Displacement Curves for 0.6-m and 0.9-m CIDH Piles after

Correction ............................................................................................................... 173

Figure 5.28 Cyclic Load-Displacement Curve for 0.6-m CIDH Pile after Correction. 173

Figure 5.29 Strain Distribution in Longitudinal Reinforcement for 0.6-m CIDH Pile. 174

Figure 5.30 Strain Distribution in Transverse Reinforcement for 0.6-m CIDH Pile.... 175

Figure 5.31 Rupture of Spiral Reinforcement and 3 Longitudinal Bars in A Direction176

Figure 5.32 Rupture of 2 Longitudinal Bars in C Direction ......................................... 176

Figure 5.33 Severe Damage of 0.6-m CIDH Pile between Depths 0 m and 0.6 m ...... 177

Figure 5.34 Crack Patterns along 0.6-m CIDH Pile ..................................................... 177

Figure 5.35 Static Load Displacement Curves for 0.9-m and 1.2-m CIDH Piles......... 178

Figure 5.36 Cyclic Load-Displacement Curve for 0.9-m CIDH Pile ........................... 178


Figure 5.38 Crack Patterns along 0.9-m CIDH Pile at Depths between (a) 0 m and 1.2 m,

and (b) 0.9 m and 2.4 m .......................................................................................... 180

Figure 5.39 Static Load Displacement Curve for 0.4-m CIDH Piles ........................... 181

Figure 5.40 Cyclic Load-Displacement Curve for 0.4-m CIDH Pile ........................... 181


Figure 5.42 Rupture of Reinforcing Steels of 0.4-m CIDH Pile at Depth of 0.3 m ..... 183

xviii

Figure 5.43 Crack Patterns along 0.4-m CIDH Pile at Depths between 0 m and 1.2 m183

Figure 5.44 Static Load Displacement Curves for 1.2-m CIDH Piles.......................... 184

Figure 5.45 Cyclic Load-Displacement Curves for 1.2-m CIDH Piles ........................ 184

Figure 5.46 Strain Distribution in Longitudinal Reinforcement for 1.2-m CIDH Pile

(No.1) ...................................................................................................................... 185


(No.2) ...................................................................................................................... 186

Figure 5.48 Crack Patterns along 1.2-m Pile ( No.2) at Depths between (a) 0.75 m and

1.5 m, and (b) 1.5 m and 4.5 m............................................................................... 187

Figure 5.49 Normalized Strain vs. Ratio of Depth to Pile Diameter ............................ 188

Figure 5.50 Cyclic Load-Displacement Curves for a) 0.4-m Pile, b) 0.6-m Pile, c) 0.9-m

Pile, and (d) 1.2-m Piles.......................................................................................... 189

Figure 6.1 Numerical Soil-Pile System Model for Simple Two-Layer System ........... 216

Figure 6.2 Determination of Shear Wave Velocity Profile (a) Travel Time Plot and (b)

Shear Wave Velocity .............................................................................................. 217

Figure 6.3 Ratio of Computed to Measure Natural Frequency vs. Pile Diameter for

Simple Two-Layer Soil Profile (Kind vs. Kdep) ........................................................ 218


Simple Two-Layer Soil Profile (Kind vs. Kfin) ......................................................... 218


Increasing Stiffness with Depth Soil Profile........................................................... 219


Increasing Stiffness with Depth Soil Profile (After increasing soil spring stiffnesses)

................................................................................................................................. 219

Figure 6.7 Comparison of Measured and Computed Damping Ratios........................ 220

Figure 6.8 Example of Curvature Calculation from Strain Gauge Data (Extracted Data

from 1.2-m CIDH Pile (No-1)) ............................................................................... 221

Figure 6.9 Moment-Curvature Relationships for 0.4-m CIDH Pile (a) Entire Curve, and

(b) Before Yielding ................................................................................................. 222

xix







Figure 6.13 Back-Calculated p-y Curves for 0.4-m CIDH Pile................................... 226

Figure 6.14 Comparison of Test Results and Analysis Using Back-Calculated p-y

Curves for 0.4-m CIDH Pile (a) Load-Displacement Curve, and (b) Moment

Profiles .................................................................................................................... 227


Curves for 0.4-m CIDH Pile (a) Rotation Profiles, and (b) Displacement Profiles

................................................................................................................................. 228




Profiles .................................................................................................................... 230



................................................................................................................................. 231




Profiles .................................................................................................................... 233



................................................................................................................................. 234

Figure 6.22 Back-Calculated p-y Curves for 1.2-m CIDH Pile (No.1) ....................... 235

xx


Curves for 1.2-m CIDH Pile (No.1) (a) Load-Displacement Curve, and (b) Moment

Profiles .................................................................................................................... 236


Curves for 1.2-m CIDH Pile (No.1) (a) Rotation Profiles, and (b) Displacement

Profiles .................................................................................................................... 237

Figure 6.25 Back-Calculated p-y Curves for 1.2-m CIDH Pile (No.2) ........................ 238


Curves for 1.2-m CIDH Pile (No.2) (a) Load-Displacement Curve, and (b) Moment

Profiles .................................................................................................................... 239


Curves for 1.2-m CIDH Pile (No.2) (a) Rotation Profiles, and (b) Displacement

Profiles .................................................................................................................... 240

Figure 6.28 Comparison of p-y Curves for Different Pile Diameters at Various Depths

................................................................................................................................. 241

Figure 6.29 Comparison between Measured and Computed Load-Displacement Curves

in Inelastic Range for 0.4-m CIDH Pile.................................................................. 242






in Inelastic Range for 1.2-m CIDH Pile (No.1) ...................................................... 243


in Inelastic Range for 1.2-m CIDH Pile (No.2) ...................................................... 244

Figure 6.34 Proposed Methodology for Constructing p-y Curves for Weakly Cemented

Sand......................................................................................................................... 245

Figure 6.35 Example of Characteristic of Proposed p-y Curves for 0.4-m Pile at Various

Depths ..................................................................................................................... 246

xxi

Figure 6.36 Example of Characteristic of Proposed p-y Curves for Various Pile

Diameters at Depth of 0.9 m................................................................................... 246

Figure 6.37 Comparison of Test Results and Analysis Using Proposed p-y Curves for

0.4-m CIDH Pile (a) Load-Displacement Curve, and (b) Moment Profiles.......... 247






1.2-m CIDH Pile (No.1) (a) Load-Displacement Curve, and (b) Moment Profiles

................................................................................................................................. 250

Figure 6.41 Modified Moment-Curvature Relationships for Effect of Soil Confinement

(a) 0.4-m Pile, and (b) 0.6-m Pile ........................................................................... 251


using Modified Moment-Curvature Relationship for 0.4-m CIDH Pile................. 252



Figure 6.44 Modified Moment-Curvature Relationships for Effect of Soil Confinement

(a) 0.9-m Pile, and (b) 1.2-m Pile ........................................................................... 253




using Modified Moment-Curvature Relationship for 1.2-m CIDH Pile (No.1) ..... 254

Figure 6.47 Relationship of Equivalent Transverse Reinforcement due to Soil

confinement............................................................................................................. 255

Figure 6.48 Results of Lateral Load Test on 0.6-m Pile............................................... 256

Figure 6.49 Comparison of Theoretical Shear Capacity with Experimentally Observed

Shear ....................................................................................................................... 257

xxii

Figure 7.1 Comparison of Back-Calculated p-y Curves with Sand p-y Curves (Reese et

al 1974; API 1987) for Depths 0 to 1.5 m .............................................................. 268

Figure 7.2 Comparison of Back-Calculated p-y Curves with Sand p-y Curves (Reese et

al 1974; API 1987) for Depths 1.8 to 3.3 m ........................................................... 269

Figure 7.3 Computed Load-Displacement Curves using Sand p-y Curves (Reese et al

1974; API 1987) Compared to Measured Response (a) 0.4-m Pile, (b) 0.6-m Pile,

(c) 0.9-m Pile, and (d) 1.2-m Pile (Pile No.1)......................................................... 270

Figure 7.4 Comparison of Load-Displacement Curves using Sand p-y Curves (API

1987) and Proposed p-y Curves for (a) 1.8-m Pile, (b) 2.4-m Pile ......................... 271

Figure 7.5 Predicted Pile Head Displacement, Maximum Moment, and Depth to

Maximum Moment Using Sand p-y Curves (Reese et al. 1974) Compared to

Response Obtained Using Back-Calculated p-y Curves for Different Pile Diameters

(a) Pile Head Displacement, (b) Maximum Moment, and (c) Depth to Maximum

Moment ................................................................................................................... 272


Maximum Moment Using Sand p-y Curves (API 1987) Compared to Response

Obtained Using Back-Calculated p-y Curves for Different Pile Diameters (a) Pile

Head Displacement, (b) Maximum Moment, and (c) Depth to Maximum Moment

................................................................................................................................. 273

Figure 7.7 Comparison of Back-Calculated p-y Curves with Cemented Sand p-y Curves

(Ismael 1990) for Depths 0 to 1.5 m....................................................................... 274

Figure 7.8 Comparison of Back-Calculated p-y Curves with Cemented Sand p-y Curves

(Ismael 1990) for Depths 1.8 to 3.3 m.................................................................... 275

Figure 7.9 Computed Load-Displacement Curves using Cemented Sand p-y Curves

(Ismael 1990) Compared to Measured Response (a) 0.4-m Pile, (b) 0.6-m Pile, (c)

0.9-m Pile, and (d) 1.2-m Pile (Pile No.1) .............................................................. 276


Maximum Moment Using Cemented Sand p-y Curves (Ismael 1990) Compared to


xxiii


Moment ................................................................................................................... 277

Figure 7.11 Comparison of Back-Calculated p-y Curves with Silt p-y Curves (Reese

and Van Impe 2001) for Depths 0 to 1.5 m ............................................................ 278

Figure 7.12 Comparison of Back-Calculated p-y Curves with Silt p-y Curves (Reese

and Van Impe 2001) for Depths 1.8 to 3.3 m ......................................................... 279

Figure 7.13 Computed Load-Displacement Curves using Silt p-y Curves (Reese and

Van Impe 2001) Compared to Measured Response (a) 0.4-m Pile, (b) 0.6-m Pile, (c)

0.9-m Pile, and (d) 1.2-m Pile (Pile No.1) .............................................................. 280


Maximum Moment Using Silt p-y Curves (Reese and Van Impe 2001) Compared to



Moment ................................................................................................................... 281


Maximum Moment Using Existing p-y Curves Compared to Response Obtained

Using Back-Calculated p-y Curves for 0.4-m Pile (a) Pile Head Displacement, (b)

Maximum Moment, and (c) Depth to Maximum Moment ..................................... 282











xxiv



Figure A-1 Results of Gradation Analysis (Borehole BH-1)........................................ 290

Figure A-2 Results of Gradation Analysis (Borehole BH-1, Continued)..................... 291



Figure A-5 Results of Gradation Analysis (Borehole BH-2)........................................ 294





Figure A-10 Results of Gradation Analysis (Borehole BH-2, Continued)................... 299

xxv

List of Tables

Table 2.1 Summary of Elastic Solutions for Laterally Loaded Pile for the Case of

Constant Soil Modulus with Depth (after Poulos, 1971).......................................... 37


Constant Soil Modulus with Depth (after Davies and Budhu, 1986) ....................... 38


Linearly Increasing Soil Modulus with Depth (after Budhu and Davies, 1988) ...... 39

Table 2.4 Summary of Definition and Dimension of Terms Used in Analysis of Laterally

Loaded Piles.............................................................................................................. 40

Table 2.5 Summary of Solutions for Laterally Loaded Pile due to Horizontal Loading for

the Case of Constant Subgrade Reaction (Hetenyi, 1946)........................................ 41

Table 2.6 Summary of Solutions for Laterally Loaded Pile due to Moment Loading for

the Case of Constant Subgrade Reaction (Hetenyi, 1946)........................................ 42

Table 2.7 Summary of Procedure in Developing Soft Clay p-y Curves (Matlock, 1970)43

Table 2.8 Summary of Procedure in Developing Stiff Clay with Free Water p-y Curves

(Reese et al., 1975) ................................................................................................... 44

Table 2.9 Summary of Procedure in Developing Stiff Clay with No Free Water p-y

Curves (Welch and Reese, 1972;and Reese and Welch, 1975) ................................ 45

Table 2.10 Summary of Procedure in Developing Sand p-y Curves (Reese et al., 1974)46

Table 2.11 Summary of Procedure in Developing API Sand p-y Curves (API, 1987).... 47

Table 2.12 Summary of Procedure in Developing Cemented Sand p-y Curves (Ismael,

1990) ......................................................................................................................... 48

Table 2.13 Summary of Procedure in Developing Silt p-y Curves (Reese and Van Impe,

2001) ......................................................................................................................... 49

Table 2.14 Summary of Case Histories of Laterally Loaded Single Piles....................... 50

Table 4.1 Minimum Transverse Reinforcement Required by Bride Design Specifications

(Caltrans 2000)........................................................................................................ 105

Table 4.2 Summary of Average Concrete Strengths for CIDH Piles ........................... 105

xxvi

Table 4.3 Summary of Locations of Strain Gauges and Tiltmeters for Each Test Pile 106

Table 4.4 Summary of Testing Program for Vibration Testing for 0.4-m CIDH Pile.. 107

Table 4.5 Summary of Testing Program for Vibration Testing for 0.6-m CIDH Pile.. 108

Table 4. 6 Summary of Testing Program for Vibration Testing for 0.9-m CIDH Pile. 108

Table 4.7 Summary of Testing Program for Vibration Testing for 1.2-m CIDH Pile

(No.1) ...................................................................................................................... 109


(No.2) ...................................................................................................................... 110

Table 5.1 Summary of Natural Frequencies of Soil-Pile Systems from Ambient and

Impact Vibration Tests............................................................................................ 156

Table 5.2 Summary of Natural Frequencies and Damping Ratios of Soil-Pile Systems

from Forced Vibration Tests................................................................................... 157

Table 5.3 Summary of Damping Ratios of Soil-Pile Systems from Impact Vibration

Tests ........................................................................................................................ 158

Table 6.1 Summary of Pile and Soil Properties Used in Natural Frequency Computation

for Simple Two-Layer Soil System ........................................................................ 215

Table 6.2 Summary of Measured and Computed Natural Frequency for Simple 2-Layer

System..................................................................................................................... 215

Table B.1 Summary of Soil Properties at Charter School Site ..................................... 301

Table B.2 Summary of Soil Properties at East Campus Utilities Plant Test Site ......... 302

Table C.1 Summary of Soil Properties at UCSD Cancer Center Building Project ....... 304

Table C.2 Summary of Soil Properties at UCSD EBU 3 and EBU 4 Site.................... 306

Table C.3 Summary of Soil Properties at Gilman Drive Parking Structure Site.......... 307

1

Chapter 1 INTRODUCTION

Integral pile shaft-columns (Figure 1.1) have been increasingly used for bridge

foundations in California because of comparative economy of construction of large

diameter of Cast-In-Drilled-Hole (CIDH) piles compared to driven piles with pile cap

footings. In addition, the use of large diameter CIDH pile can solve the problem of

adding new structures in confined area, which do not allow either driven piling or large

spread footings. The understanding of soil-structure interaction characteristics,

particularly lateral pile response, has therefore become a major concern for the design of

large diameter CIDH piles.

One of the most widely accepted methods used in analyzing the response of

laterally loaded piles is the Winkler spring method in which the soil resistance along the

pile is modeled using a series of nonlinear soil springs, widely known as p-y curves.

Most of the existing standard p-y curves (e.g., for sand, see Reese et al., 1974; for soft

clay, see Matlock, 1970; for stiff clay above water table, see Reese and Welch, 1975; and

for stiff clay below water table, see Reese et al., 1975) were developed based on results

of full-scale lateral load tests on a relatively small range of pile diameters and theory was

then extrapolated to use for other diameter sizes. Therefore, the degree of accuracy in

predicting the lateral responses for a wide range of pile diameters especially for large pile

diameters is still questionable. Furthermore, recent research by Carter (1984) and Ling

(1988) showed that the soil response actually appears to become stiffer as the pile

diameter increases and suggested that the initial modulus of subgrade reaction, the initial

stiffness of p-y curves, should increase linearly with the pile diameter. This is in conflict

with the commonly assumed Terzaghi model (Terzaghi, 1955), in which the modulus of

subgrade reaction is considered to be independent of pile diameter. It is therefore

essential and beneficial to the engineering profession to evaluate the effect of pile

diameter on modulus of subgrade reaction. If the pile diameter has a significant effect on

modulus of subgrade reaction, the construction cost of foundations can be substantially

decreased when large diameter piles are considered in the design.

2

In-Ground Plastic Hinge

CIDH Pile

Column

Mmax

- Moment +

Figure 1.1 Integral Pile-Shaft Column and Moment Profile

It is commonly known that by implementing the integral pile-shaft column, the

possibility of an in-ground plastic hinge exists, if the column is continued as a pile shaft

extension with the same diameter into the ground (Figure 1.1). Therefore, the

understanding of inelastic behavior of the pile becomes another important issue. Several

experiments on inelastic behavior of piles have been carried out; however, most of them

were tested in the laboratory without soil for confinement. Budek (1997) conducted

experiments on the inelastic behavior of CIDH piles by modeling the effect of soil

confinement with a series of rubber saddles. The test results indicated that this external

confinement, which can be provided by soil, plays a significant role in enhancing the

3

plastic response of CIDH piles and that only moderate levels of transverse reinforcement

are needed for adequate seismic performance. However, the results from full-scale lateral

pile load tests in the actual soil are needed to verify the results of the laboratory testing

before widely implementing this finding in future design.

1.1 Objectives of Research

A research program has been carried out to investigate the effect of pile diameter

on modulus of subgrade reaction, as well as the inelastic performance of CIDH piles

using the full-scale lateral pile load test. Specifically, the objectives of this research

study can be summarized as follows:

1. To study the effect of pile diameter on pile response using both numerical

analyses via the 3-D finite element approach and the results from full-scale

lateral load tests on different diameters of CIDH piles.

2. To develop the methodology for constructing the p-y curves for dense weakly

cemented sand, taking the pile diameter effects into account.

3. To evaluate the seismic performance of CIDH piles due to the effect of

external confinement from soil.

4. To evaluate the capability of existing p-y curves in predicting the responses of

laterally loaded piles in weakly cemented sand for a wide range of pile

diameters using the results from the full-scale lateral load tests.

To achieve this goal, the 3-D finite element models for soil-pile interaction were

first developed to study the pile diameter effect on soil response using both linear and

nonlinear soil models. This provided a general understanding of the diameter effect using

the available analytical tools before conducting the full-scale experiments. Cast-In-

Drilled-Hole (CIDH) piles with diameters ranging from 0.4 m to 1.2 m were then

installed and tested at the University of California, San Diego (UCSD). The test site,

which consisted of dense weakly cemented sand, was chosen to represent the soil that is

4

often found along the coast of Southern California. The p-y curves for this particular type

of soil deposit for a wide range of pile diameters have never been developed.

Two different types of testing were performed in this study including vibration

testing and lateral load testing. The vibration testing was performed so as to obtain the

dynamic properties of soil-pile system and study the responses of the system at small

strain levels where the soil properties remain linear elastic. The test results were used in

studying the effect of pile diameter on initial modulus of subgrade reaction, the initial

stiffness of p-y curve. The lateral load test under static loading was performed with the

aim of developing the p-y curves for different pile diameters, and therefore the pile

diameter effect at larger strain level can be evaluated. The seismic performance of CIDH

piles due to the effect of external confinement from the soil were assessed using the

results from cyclic lateral pile load tests. Expecting the improvement from the

confinement provided by the soil, the amount of transverse reinforcement used in the

CIDH pile test specimens was therefore chosen to be less than that suggested by Bridge

Design Specification (Caltrans, 2000).

Furthermore, the possibility of the use of various types of existing p-y curves to

predict the pile response in weakly cemented sand was assessed by comparing the

computed responses with the measured responses from the results of full-scale lateral

load tests

1.2 Organization of Report

The following outlines the organization of this report.

Chapter 1 Introduction – Provides a brief description on the significance of

research on the effect of pile diameter on modulus of subgrade reaction, a summary of

research objectives, and an outline of this report.

5

Chapter 2 Literature Review – Provides a review on current methods

available in predicting the lateral pile response with discussions on the advantages and

limitations of each method, the concept of p-y curves and types of p-y curves currently

available, as well as a summary of research on pile diameter effect on p-y curves. A

summary of full-scale lateral pile load tests conducted by several researchers were also

given. In addition, a review on the research on the behavior of weakly cemented soil, as

well as inelastic behavior of piles, is provided.

Chapter 3 Evaluation of Pile Diameter Effect Using 3-D Finite Element

Method – Presents the results of a study of pile diameter effect on pile response using 3-

D finite element method. Both linear and nonlinear soil models were incorporated in this

study.

Chapter 4 Full-Scale Testing – Provides geotechnical information about the

test site and the description of test piles. The test arrangement, testing programs, and

testing procedures on both vibration and lateral load tests are discussed.

Chapter 5 Test Results – The dynamic properties of the soil-pile system

based on the results of various types of vibration tests are presented and discussed. This

is followed by the results of full-scale lateral load tests under both static and cyclic

loadings which include the load-displacement curves, and strain gauge data.

Chapter 6 Analysis of Test Results – The evaluation of the effect of pile

diameter on p-y curves based on the experimental results are presented. This included the

effect of pile diameter on the initial modulus of subgrade reaction using the results from

vibration tests. The p-y curves for each pile diameter were back-calculated using the

results from lateral load tests. The p-y curves for various pile diameters were then

compared to provide insight into the effect of pile diameter on p-y curves. In addition,

the methodology to construct the p-y curves for the soil type tested in this study was

6

proposed. Finally, the effect of soil confinement in enhancing the inelastic behavior of

the piles was quantitatively evaluated.

Chapter 7 Implementation of Existing p-y Curves for Weakly Cemented

Sand– Several existing p-y curves, including sand p-y curves and cemented sand p-y

curves were used to predict the experimental test results to evaluate its capability in

predicting the pile response for a wide range of pile diameters.

Chapter 8 Summary and Conclusions– Provides the summary and

conclusions of this research study.

7

Chapter 2 LITERATURE REVIEW 2.1 Introduction The problem of the laterally loaded pile was originally of particular interest in the

offshore industry. Lateral loads from wind and waves are frequently the most critical

factor in the design of such structures. Solutions of the general problem also apply to a

variety of onshore cases including pile supported earthquake resistance structures, power

poles, and pile-supported structures which may be subjected to lateral blast forces or

wind forces.

In the design of pile foundations against lateral loading, two criteria must be

satisfied: 1) the pile must have an adequate factor of safety against the maximum lateral

loading that might be applied to it, and 2) the deflection that occurs due to a working load

must be in an acceptable range that superstructure can withstand (Poulos and Davis,

1980). A common procedure used for analysis and design of piles under lateral loading

in earthquake engineering is to conduct a pushover analysis to determine the load-

displacement relationship of the structure. The design-basis lateral load used for pile

design is calculated based upon an appropriate value of spectral displacement at the

structure’s fundamental-mode period and damping ratio.

Several analytical methods have been proposed that attempt to model lateral pile

response, none of which can completely account for all factors that influence lateral soil-

pile interaction. The earliest and simplest representation problem was that of a

transversely loaded thin elastic beam, supported by a series of linear springs (Winkler

spring method) acting along the length of the beam (Winkler, 1867; Hetenyi, 1946;

Barber, 1953; Matlock and Reese, 1960; and Davisson and Gill, 1963). Because of the

analytical simplicity, this method is widely used in foundation engineering. However,

the response of real soil is far from elastic, and nonlinear soil response is the key factor in

the behavior of laterally loaded piles. A series of nonlinear soil spring, known as p-y

8

curves, back-calculated based on the results from full-scale lateral pile load tests were

replaced the linear soil springs for a better representation of the actual soil behavior (e.g.,

Matlock, 1970; Reese et al., 1974; Reese and Welch, 1975; Reese et al., 1975; and

Ismael, 1990). The pile nonlinearity also can be easily taken into account by using this

method. As a result, it is one of the most acceptable methods currently used in the design

of laterally loaded pile. The disadvantage of this method is, however, a neglecting of soil

continuity.

Another analysis method considers the soil as an elastic continuum and

implements a boundary element analysis to develop the solutions for analyzing the pile

response (e.g., Spillers and Stoll, 1964; Poulos, 1971 and 1973; and Banerjee and Davies,

1978). The nonlinearity of soil, such as soil reaching the ultimate bearing capacity, was

taken into account by means of modified boundary element analysis (e.g., Banerjee and

Davies, 1979; Davies and Budhu, 1986; and Budhu and Davies, 1988). However, these

solutions are limited to simple cases, such as a constant soil modulus with depth, a linear

increasing soil modulus with depth, and a simple 2-layered soil system. Application for

design of a real problem is not as flexible as the Winkler method. Furthermore, the

inelastic behavior of pile can not be properly incorporated in this method. As a result,

this method is not widely used in design.

Recently, using a finite element method to represent the soil mass seems to

become more popular due to the availability of the computational power of computers, as

well as the ability to investigate some other aspects that the previous mentioned methods

can not account for, such as stress-strain behavior in the soil mass (Desai and Appel,

1976; Randolph, 1981; Kuhlemeyer, 1979; Kooijman, 1989; Brown et al., 1989;

Trochanis et al., 1991; and Bransby, 1999). Though the method can be quite versatile,

the use has been limited primarily to research. Application of this method in design has

rarely been used due to the limitation of current constitutive soil models, as well as the

requirement of engineering time in generating the input and interpreting the results.

9

In this chapter, a summary of methods being used in lateral pile response

analyses are reviewed and the pros and cons of each method are discussed. The review

is mainly focused on the Winkler spring method, which is widely used in the current

design of bridge foundation. This is followed by a review of previous full-scale lateral

pile load tests on single piles under static and cyclic loadings. Furthermore, inelastic

behavior of the concrete pile based on the laboratory and full-scale testing found in the

literatures are presented. Finally, research on the behavior of cemented sand, a soil type

considered in this research study, is reviewed.

2.2 Methods in Predicting Lateral Pile Responses 2.2.1 Elastic Continuum using Boundary Element Method

The boundary element method was used extensively between 1960 and 1980 to

solve the problem of piles subjected to lateral loading. In this method, the fundamental

solution needs to be solved first, which gives the response of a point at the interior of the

soil mass as a result of the application of load at another point of the soil mass. Mindlin

(1936) presented the solutions of horizontal displacements caused by a horizontal point

load within the interior of semi-infinite, elastic, isotropic homogeneous mass. This

solution was used by many researchers (e.g., Spillers and Stoll, 1964; Poulos, 1971,

Banerjee and Davies, 1978; and Davies and Budhu, 1986) to analyze the response of a

pile subjected to lateral loading. All of these analyses are similar in principle; the

differences arising largely from details in the assumptions regarding the pile action. The

accuracy of the answers is dependent on the number of element subdivided in the pile,

particularly sensitive for a very flexible pile case. The analysis of the single pile problem

by means of boundary element analysis involves discretizing the pile interface with soil

into small elements and equating the displacement of pile and soil at the center of

elements. In this process, the soil displacements are obtained through the Mindlin’s

solution.

10

For the case of a constant soil modulus with depth, which is usually used to

represent the behavior of overconsolidated clay, the solutions of pile response from both

free-head and fixed-head piles taken from works by Poulos (1971) are given in Table 2.1.

The dimensionless elastic influence factors can be obtained from graphs presented in

Figure 2.1. Another solution of lateral pile response in a constant soil modulus with

depth was also given by Davies and Budhu (1987) as summarized in Table 2.2. The

slight difference in results obtained from both methods is due to the different assumptions

being used as well as the number of pile elements considered in the analyses.

The advantage of this approach is that the continuity of the soil is taken into

account to develop the solutions of lateral pile response. However, the elastic continuum

approach is limited by several factors. Since in reality the soil is irregular and the

Young’s modulus and Poisson’s ratio change with depth, the assumption of a

homogeneous isotropic semi-infinite soil is ideal. Some researchers have proposed

solutions to account for varying soil stiffness profiles. Poulos (1973) and Banerjee and

Davies (1978) proposed solutions for a layered soil. Banerjee and Davies (1978), and

Budhu and Davies (1988) provided solutions for soil with linearly increasing soil

modulus with depth. This type of soil profile represents the behavior of sand and

normally consolidated clay. Work by Budhu and Davies is summarized in Table 2.3.

Though solutions for a variety of soil profiles have been developed, the

implementation of this method is not easy and flexible for real problems. In addition, the

behavior of the soil under large deflections is highly nonlinear. Therefore, the

assumption that the soil is linear elastic is not acceptable. This assumption is reasonable

when only the soil deforms with small strain. Furthermore, the application of this method

for the earthquake engineering problem is difficult. This method is therefore useful only

for a crude estimation or preliminary analysis due to its simplicity of calculation.

11

2.2.2 Modified Boundary Element Analyses

A modified boundary element analysis is the extension of the boundary element

method in an attempt to incorporate an elasto-plastic soil model to account for soil

yielding, particularly at the ground surface. The effect of local yield of the soil was first

outlined by Spillers and Stoll (1964), in which a limiting lateral pressure is specified for

each element of the pile and the analysis ensures that the computed pile-soil pressure

does not exceed this limiting value. A similar principle was employed by Poulos (1971)

in his study of the effect of local soil yielding on the response of a laterally loaded pile

with various distributions of soil pressures with depth.

Banerjee and Davies (1979) used incremental and iterative initial stress or initial

strain procedures in which the effect of yielding or slipping are introduced by distributing

initial stresses over volume “cells” and distributing initial tractions over slip surfaces,

respectively.

Davies and Budhu (1986) proposed a method to predict the behavior of a laterally

loaded pile by taking into account soil and pile yielding. The yielding of the soil

considered in this study includes bearing capacity failure in the compressive zone, shear

failure at the side along the soil-pile interface, and tension failure in the soil. The

solutions were suitable for heavily overconsolidated clay where the soil strength profile

can be generally assumed to be constant with depth. Budhu and Davies (1988)

implemented the same principle as used in a constant modulus with depth to further

develop the solutions to use for soft clay and sand where the soil strength linearly

increases with depth.

Though researchers have attempted to incorporate the complexity of soil through

the use of modified boundary element analyses, such as taking into account soil yielding,

layered soil, and various distributions of soil modulus with depth, this type of analysis is

still not sufficiently flexible to model the problem of a laterally loaded pile in reality.

12

Furthermore, the application to the earthquake engineering industry such as dynamic

analysis is difficult. Other methods which seem to be more practical in the engineering

practice are discussed in the following sections.

2.2.3 Finite Elements for Soil

In recent years, this method has become more extensively used due to the

availability of the computational power of computers. The main advantages of this

method are that the continuity of soil, as well as the soil nonlinearity, can be taken into

account. This is an idealized method for studying the response of laterally loaded piles in

the future because this method is very powerful and most of the aspects that other

methods can not be investigated can be studied via finite element method such as the

stress and strain in the soil mass, influence of gapping, and the effect of construction

sequencing. However, its accuracy still depends on the ability to predict the soil

properties and also the accuracy of constitutive soil models. The proper constitutive soil

models for this type of analyses need to be developed and also verified with the results

from full-scale and/or centrifuge testing. Another disadvantage of this method is the high

computation time, especially in the case of 3-D analyses. Currently, the finite element

method has been predominantly used in research on laterally loaded piles, but the

application of this method has rarely been used in the design due to the limitation of

current constitutive soil models, as well as the requirement of engineering time in

generating the input and interpreting the results.

There are several examples of research on laterally loaded piles using the finite

element method. Desai and Appel (1976) developed a 3-D finite element solution for the

laterally loaded pile problem. Randolph (1981) and Kuhlemeyer (1979) introduced a

more economical method: using the finite element method in conjunction with Fourier

techniques. Randolph (1981) conducted a parametric study on the response of laterally

loaded piles embedded in the elastic soil continuum with constant and linear increasing

13

soil modulus with depth. Algebraic expressions fitted to the results from the parametric

study to predict lateral pile response were proposed.

Kooijman (1989) and Brown et al. (1989) used three-dimensional finite elements

to develop p-y curves. Trochanis et al. (1991) examined the effect of nonlinear soil

behavior on the axial and lateral pile responses using a three-dimensional finite element

analysis. Bransby (1999) implemented a 2-D finite element analysis to find load-transfer

relationships for laterally loaded pile and suggested that these curves could be used as p-y

curves in the analysis of laterally loaded piles.

2.2.4 Winkler Method and the Concept of p-y Curves

The Winkler method, or sometimes known as the subgrade reaction method,

currently appears to be the most widely used in a design of laterally loaded piles. The

method was first introduced by Winkler (1867) to analyze the response of beams on an

elastic subgrade by characterizing the soil as a series of independent linearly-elastic soil

springs. Since then, this concept has been extensively employed for the laterally loaded

pile problem. The concept of this method is graphically illustrated in Figure 2.2.

One of the great advantages of this method over the elastic continuum method is

that the idea is easy to program in the finite difference or finite element methods and that

the soil nonlinearity and multiple soil layers can be easily taken into account. The

concept can be easily implemented in dynamic analysis. In addition, the computational

cost is significantly less than the finite element method. However, the obvious

disadvantage of this method is the lack of continuity; real soil is at least to some extent

continuous.

The term of subgrade reaction indicates the pressure, P, per unit area of the

surface of the contact between a loaded beam or slab and the subgrade on which it rests

14

and on to which it transfers the loads. The coefficient of subgrade reaction, k, is the ratio

between the soil pressure, P, at any given point of the surface of contact and the

displacement, y, produced by the load application at that point:

yPk = (2.1)

To implement this concept for a laterally loaded pile, the above equation (2.1) has

been modified frequently (e.g. Reese and Matlock, 1956; and Davisson and Gill, 1963) as

ypK = (2.2)

where K is the modulus of subgrade reaction (F/L2) and p is the soil reaction per unit-

length of the pile (F/L). It should be noted that the dimensions of each variable are given

in parentheses. Since these terms are often confused in the literature, they are

summarized in Table 2.4 to make this report easier to follow.

With the subgrade reaction concept, the lateral pile response can be obtained by

solving the forth order differential equation as:

04

4

=+ Kydz

ydIE pp (2.3)

where Ep is the modulus of elasticity of the pile, Ip is the moment of inertia of the pile,

and z is depth.

Solutions of Eq. (2.3) can be obtained either analytically or numerically.

Analytical solutions are only available in the case of constant modulus of subgrade

15

reaction with depth. For other subgrade reaction distribution, the solutions are

conveniently solved by using the finite difference method.

Hetenyi (1946) provided solutions for a variety of infinite beams on an elastic

Winkler subgrade by solving analytically the governing equations. The solutions can be

applied to analyze the response of a laterally loaded pile with a constant subgrade

reaction. Table 2.5 and Table 2.6 summarize the solutions of lateral pile responses due to

the horizontal loading and moment at the pile head, respectively. Barber (1953)

provided the solutions to determine the deflections and rotation at the ground surface

using the convenient plots for cases of constant soil modulus of subgrade reaction, as

well as the linearly increasing soil modulus of subgrade reaction with depth. Several

functions of distribution of modulus of subgrade reaction with depth (i.e., polynomial

function and power function) have been considered by Matlock and Reese (1960).

Matlock and Reese give the solutions for a special case soil profile where the modulus of

subgrade reaction has some finite value at the ground surface and continues to increase

linearly with depth.

Davisson and Gill (1963) extended the subgrade reaction theory to analyze the

behavior of laterally loaded piles in a two-layer soil system for both free and fixed head

conditions and provided the results in non-dimensional forms.

The values of modulus of subgrade reaction can be obtained using the in-situ

testing, such as the plate loading test. For practical purposes, Terzaghi (1955)

recommended the rough estimate values of coefficient of subgrade reaction for stiff clay

and sand to be used for analyzing pile response using subgrade theory. He stated that the

linear relationship between the soil pressure and displacement was valid for values of the

soil pressure that were smaller than about one-half of the bearing stress.

16

Another method in estimating the modulus of subgrade reaction is the use of the

equation proposed by Vesic (1961). Vesic provided a relationship between the modulus

of subgrade reaction, K, used in the Winkler spring problem and the material properties in

the elastic continuum problem as

12/14

2 )1(65.0

⎥⎥⎦

⎤

⎢⎢⎣

⎡

−=

pp

s

s

s

IEDEE

Kµ

(2.4)

where Es = soil modulus of elasticity, µs = Poisson’s ratio of the soil, D = pile diameter,

and EpIp = flexural rigidity of the pile. By knowing the soil modulus of elasticity from

the laboratory or field testing, as well as the pile property, the modulus of subgrade

reaction can be estimated.

2.2.4.1 Concept of p-y Curves

All of the solutions based on subgrade reaction theory mentioned in the previous

sections are valid only for a case of linear soil properties. In reality, the relationship

between soil pressure per unit pile length p and deflection y is nonlinear. Taking the

nonlinearity of soil into account, the linear soil springs are replaced with a series of

nonlinear soil springs, which represent the soil resistance-deflection curve so called, “p-

y” curve. The p-y curves of the soil have been developed based on the back analysis of

the full scale lateral pile load test. This concept was first developed by McClelland and

Focht (1958).

The concept of a p-y curve can be defined graphically as shown in Figure 2.3. It

was assumed that the pile was perfectly straight prior to driving and there was no bending

of the pile during driving. The soil pressure acting against the pile prior to loading can be

reasonably assumed to be uniform, Figure 2.3a. The resultant pressure for this condition

is zero. If the pile is loaded with a given lateral deflection as shown in Figure 2.3b, a net

17

soil reaction will be obtained by the integration of the soil pressures around the pile

giving the unbalanced force per unit length of the pile. This process can be repeated in

concept for a series of deflections resulting in a series of forces per unit length of pile

which may combine to form a p-y curve. In a similar manner, the sets of p-y curves along

the pile as shown in Figure 2.4 can be obtained. If such a set of curves can be predicted,

the yield pile deflection, pile rotation, bending moment, shear, and soil reaction for any

load capable of being sustained by the pile can be obtained by solving the beam equation.

The series of p-y curves greatly depends upon the soil type. The p-y curves can

be obtained experimentally by conducting the full scale testing of instrumented piles in

the type of soil deposit interested. Figure 2.5 presents the methodology in developing the

p-y curves. The bending moment diagram along the pile can generally be computed by

the product of pile curvatures, which are computed from the measured strain along the

pile, with the known pile stiffness. Double differentiation of the bending moment

diagram produces the soil reaction curve. The deflection along the pile can be obtained

by double integration of the curvature diagram. Therefore, the soil reaction versus the

deflection of the pile, p-y curve, at a given depth can be obtained.

Though the Winkler method neglects soil continuity, a disadvantage to a

considerable extent, it has been overcome through calibrating p-y curves to full-scale test

results. However, many factors which influence the behavior of laterally loaded piles

have been lumped into the characteristic shape of the p-y curves and difficult to separate

due to the limit number of the full-scale testing. Some of parameters which may have a

significant effect on the pile response have not been investigated systematically such as

the pile diameter effect, the effect of soil gapping, and the validity of using these p-y

curves for a rigid pile case. Further research on these issues needs to be investigated in

order to improve the existing p-y curves for the wider range of application.

18

Several researchers have proposed methods to construct p-y curves for various

soil types based upon back-computation from full-scale test results. The following

paragraphs presents the brief description of each p-y curves currently available in the

industry. Most of these p-y curves have been incorporated in the commercial programs in

analyzing behavior of laterally loaded pile, such as COM624P (Wang and Reese, 1993),

LPILE (Reese et al., 2000), and FLPIER (University of Florida, 1996).

2.2.4.2 Soft Clay p-y Curves

Matlock (1970) conducted full-scale lateral load tests on a 0.3-m diameter

instrumented steel pipe pile embedded in soft clay deposit at Lake Austin, Texas. The

methodology to develop the p-y curves was proposed based on the back-computed p-y

curves from the test results. Figure 2.6a presents the characteristic shape of the soft clay

p-y curves for static loading case which can be represented by using cubic parabola

relationship as:

31

50

5.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

yy

pp

u

(2.5)

where: pu = ultimate soil resistance which is related to the undrained shear strength of the

soil as well as a function of depth, and y50 = the soil displacement at one-half of ultimate

soil resistance. Figure 2.6b shows characteristic of p-y curves under cyclic loading. The

main difference between static and cyclic loading is that the soil resistance at large strain

level is deteriorated due to the effect of cyclic loading. A summary of procedure in

developing the soft clay p-y curves for both static and cyclic loading is given in Table 2.7

2.2.4.3 Stiff Clay p-y Curves below Water Table

Reese et al. (1975) performed lateral load tests on two 0.6-m diameter steel pipe

piles embedded in stiff clay under water table at Manor, Texas. The characteristic shapes

19

of these p-y curves for both static and cyclic loading are presented in Figure 2.7. The

shape of the p-y curve shows a very large loss of soil resistance much more than has been

observed elsewhere, probably because the soil at Manor site was expansive and continued

to imbibe water as cycling progressed. The use of these p-y curves will therefore yield a

conservative estimate of pile response. The parameters, which control the characteristic

shape of the p-y curves, are similar to those of soft clay p-y curves as mentioned earlier.

Table 2.8 summarizes the methodology for developing the p-y curves for stiff clay below

water table for both static and cyclic loadings.

2.2.4.4 Stiff Clay p-y Curves above Water Table

Welch and Reese (1972) conducted lateral load tests at a site in Houston, Texas

with a 0.76-m diameter bored pile and proposed the detailed procedure in constructing p-

y curves in stiff clay above water table. The characteristic shape of p-y curves are

somewhat similar to the p-y curves for soft clay (Matlock, 1970), but stiffer due to the use

of the forth degree of parabola relationship to represent the curve. Furthermore, unlike

stiff clay under water table, no soil softening is observed on the characteristic shape of p-

y curves in stiff clay without water table as presented in Figure 2.8. The soil resistance

for cyclic p-y curves decreases as the number of the cycles of load application increases.

Table 2.9 summarizes a procedure in constructing the p-y curves for this type of soil.

2.2.4.5 Sand p-y Curves

Reese et al. (1974) proposed the procedure in constructing the p-y curves for sand

under static and cyclic lateral loadings. The procedure was developed from the results of

tests at Mustang Island on two 0.6 m diameter, flexible driven piles embedded in a

deposit of submerged, dense, fine sand (Cox et al., 1974). The characteristic shape of the

p-y curve is highly nonlinear and can be described by three straight line portions and a

parabolic curve as illustrated in Figure 2.9. The method in developing the p-y curves

involves the estimation of initial modulus of subgrade reaction and ultimate soil

20

resistance. The suggested values of initial modulus of subgrade reaction for different

relative densities of sand are given by Reese et al. (1974). This initial straight-line

portion of the curves (where Es is linearly with deflection) governs for only small

deflections. Therefore, the initial slope of the p-y curve influences analyses for only very

small load level.

The ultimate soil resistance near the ground surface is developed based on a

wedge type failure theory; whereas, that at some distance below the ground surface was

derived based on the flow failure model as presented in Figure 2.10.

It was found that by using the equations for estimating the soil resistance based on

the theoretical developed above, the ultimate soil resistance was much smaller than the

experimental one. Therefore, Reese et al. (1974) modified the ultimate soil resistance by

introducing an empirical adjustment factor A as presented in Figure 2.11a to bring the

two quantities into agreement. Since the theory developed to predict the ultimate soil

pressure did not match the experimental p-y curves, extrapolating this method for

different soil strengths and/or pile diameters should be investigated.

2.2.4.6 API Sand p-y Curves

The method in developing the p-y curve based on the procedure proposed by

Reese et al. (1974) is quite tedious. O’Neill and Murchison (1983) proposed a simplified

method for sand p-y curves, which also yielded the results with relatively good accuracy

compared to the original p-y curves. These modified p-y curves were accepted by the

American Petroleum Institute (API) committee and officially used extensively. In the

API method, the sand p-y curves were simplified using a hyperbolic tangent function to

describe the characteristic shape of the p-y curves as presented in Table 2.11. The

lengthy equations for determining the ultimate soil pressure were simplified by the use of

three coefficients C1, C2 and C3 as a function of the friction angle, which can be simply

obtained from the graph as presented in Figure 2.12a. The initial modulus of subgrade

21

reaction constant was proposed in the graphical form as presented in Figure 2.12b. The

experimental adjustment factor A for the static load test was simplified using a linear

equation; therefore, a difference in the empirical adjustment factor A was expected and

therefore resulted in a slight difference in ultimate soil pressure. Table 2.11 presents the

step by step in developing the API sand p-y curves.

2.2.4.7 p-y Curves for c-φ Soils

Generally, in design, the soil is usually classified into 2 different types, either

cohesive or cohesionless soils, since the theories to analyze geotechnical problems were

developed based on that concept. This practice sometimes leads to a significantly

conservative design in the case of cemented soil or silt, which always neglects the soil

resistance from the cohesion component. For the behavior of laterally loaded piles in

cemented soil, it is apparent that the cohesion from cementation will increase soil

resistance significantly, especially for soil near the ground surface.

Ismael (1990) conducted full-scale lateral load pile tests in medium dense

cemented sands on single piles and on small groups under static loading in Kuwait. All

12 tested piles were 0.3 m-diameter reinforced concrete bored piles with the pile lengths

of 3 m and 5 m. Two of them were instrumented with electric resistance strain gauges to

measure bending moment. Based on drained triaxial test results, the angle of friction and

cohesion were 35o and 20 kPa, respectively. It was shown that the predicted load-

displacement characteristics based on sand p-y curves developed by Reese et al. (1974)

significantly underestimated the experimental response because it ignored the cohesion

component. Theoretical parabolic p-y curves, which accounted for both angle of friction

and cohesion component, were then proposed as presented in Figure 2.13. A summary of

the procedure used in developing cemented sand p-y curves is presented in Table 2.12

Using these p-y curves the predicted responses were in good agreement with the

experimental results.

22

The procedure proposed by Ismael indirectly showed that the cemented soil

behaves more like cohesive soil than cohesionless soil because the p-y curves as

presented in Figure 2.13 are approximated by using a cubic parabola as used in the soft

clay p-y curves (Matlock 1970).

In contrast, Reese and Van Impe (2001) believed that the behavior of c-φ soils is

closer to that of cohesionless soil than of cohesive soil. The procedure to develop p-y

curves for c-φ soil was suggested based upon procedure in developing p-y curves for

sand and ideas presented by Ismael (1990). The characteristic shape of c-φ soil p-y

curves, which is called silt p-y curves in LPILE computer program, are different from that

obtained from the cemented sand p-y curves (Ismael, 1990) in which the strain softening

appears after reaching its peak strength as presented in Figure 2.14. A summary of

developing this type of p-y curves are given in Table 2.13. It is noted that the silt p-y

curves were developed based on the theoretical basis alone without any validation from

the full-scale test results.

2.2.4.8 Hyperbolic Soil Model

Similar to the concept of p-y curves, Carter (1984) developed the simple

hyperbolic soil model (P-y curves) to represent the characteristics of soil and

implemented them in the Winkler method. The difference is that the soil pressure, P, not

the soil resistance per unit length, p, is used in this soil model. Therefore, to change this

soil model to p-y curves the soil pressure needs to be multiplied by the pile diameter.

This simple soil model can be established using only three parameters, including the

initial coefficient of subgrade reaction, ko, ultimate soil pressure, Pult, and nonlinearity

index n, as presented in Figure 2.16. The curve of hyperbolic soil model is given as:

23

⎥⎦

⎤⎢⎣

⎡−

=)( nn

ult

nult

o PPP

kPy (2.6)

where y = soil displacement at any point (L), P = soil pressure (F/L2), n = index that

controls nonlinearity (1 for sand and 0.2 for clay), ko = small strain coefficient of

subgrade reaction (F/L3), and Pult = ultimate soil pressure (F/L2). The main advantage of

this method is that one soil model can be used for both cohesive and cohesionless soil

cases. Carter (1984) implemented this soil model to predict the results of full scale pile

tests and found that a value of n = 1, seems appropriate for sand and 0.2 for clay. Six

series of pile tests analyses by Carter appears to predict the response of piles with a

similar level of accuracy that of p-y curves proposed by Reese et al. (1974).

Ling (1988) continued Carter’s work by conducting the analysis by using the

computer program developed by Carter (1984) to predict the response of full scale pile

tests from case histories. Ling found that using the hyperbolic model with the value of n

= 1 can predict the response of twenty eight full scale pile tests, both in sand and clay

with a reasonable degree of accuracy.

2.2.4.9 Effect of Pile Diameter on p-y Curves

p-y curves have been developed for various soil types which show that different

types of soils have their own characteristic shapes. Pile diameter, one of the factors

which may significantly influence the behavior of laterally loaded piles, has not yet been

systematically investigated. As can be seen from the review of various types of p-y

curves, most of the p-y curves were developed based on the results of full scale testing on

a limited number of piles due to the high cost of full-scale testing. The theory was then

developed based on that limited information and then empirically extrapolated to use for

other diameters. The degree of accuracy in predicting the pile response for a wide range

of pile diameters is therefore of interest.

24

A few studies on pile diameter effect on clay are available in the literature. No

studies have been reported on an investigation of pile diameter on p-y curves in sand.

Reese et al. (1975) back-calculated p-y curves of 0.65-m pile tested at Manor site and

used them to predict the behavior of 0.15 m diameter pile. Good agreement of moment

comparison between analysis and experiment was found; however, the computed

deflection was considerably lower than the measured one. No conclusion could be made

on the disagreement.

O’Neill and Dunnavant (1984) and Dunnavant and O’Neill (1985) conducted the

laterally laded piles with diameters of 0.27 m, 1.22 m and 1.83 m in an overconsolidated

clay site. They found that the deflection at one half of the ultimate soil pressure (y50) is

not linearly dependent on pile diameter, with the y50 getting smaller as the pile diameter

increases. This means that the pile diameter effect incorporated in the clay p-y curves is

actually less than that observed from the actual behavior. The modification on Matlock’s

p-y curves was proposed to match the agreement between measured and computed

response.

Stevens and Audibert (1979) collected published case histories on laterally loaded

piles in clay and implemented existing p-y curves proposed by Matlock (1970) and API

(1987) to analyze the pile response. They found that the computed to measured

deflection ratio is generally greater than 1 and becomes larger with increasing pile

diameter. In addition, the computed maximum moment is higher than the observed

values as much as 30%. In order to match the test results, Stevens and Audibert (1979)

suggested that the pile displacement at 50% of ultimate soil pressure should be

proportional to the square root of pile diameter, not a linear function of the pile diameter

as originally proposed by Matlock (1970). Again, this finding indicates that the actual

pile diameter effect is more than that incorporated in the soft clay p-y curves.

25

Ling (1988) performed back analysis of lateral response of pile based on a large

number of case histories on full-scale lateral pile load tests by using the hyperbolic soil

model proposed by Carter (1984). The results presented in Figure 2.17 show that the

ratio of predicted to measured deflection with respect to pile diameter using Terzaghi’s

concept in which the initial modulus of subgrade reaction is independent of pile diameter

underestimate the pile head displacement for pile diameter less than 1 m. However, it

tends to overestimate the pile head deflection when the pile diameter larger than 1 m. By

making a linear correction to the modulus of subgrade reaction suggested by Carter

(1984) and Ling (1988), the ratio between the predicted to measures is very close to 1.0.

Previous reviews show that pile diameter has some effect on the p-y curves. This

contradicts the research by Terzaghi (1955). Terzaghi explained the influence of pile

diameter on the coefficient of subgrade reaction by using the concept of a stress bulb to

show that the larger pile diameter has a deeper stress influence than the smaller one as

presented in Figure 2.18. Therefore, with an equivalent applied pressure, a larger pile

diameter encounters greater displacement with simple proportion to the pile diameter

resulting in a lower coefficient of subgrade reaction.

nk

nyP

yPk

nn

1

1

=== (2.7)

where kn, k1 = coefficient of subgrade reaction for pile diameter D and D1,respectively, n

= D/D1, and p/y1 = k1. Terzaghi concluded that the coefficient of subgrade reaction is

linearly proportional to the inverse of pile diameter. In other words, the modulus of

subgrade reaction is independent of pile diameter. Due to the contradiction of pile

diameter effect on p-y curves, more research on this area needs to be continued.

26

2.2.4.10 Development of p-y Curves for Layered Soils

The p-y curves mentioned in the preceding sections are applied for homogeneous

soil. However, the soil in reality usually consists of several soil layers. Some analytical

studies have been performed by Davission and Gill (1963), Khadilkar et al. (1973), Naik

and Peyrot (1976), and Dordi (1977) for two-layer soils to define pile length, the

thickness of the upper layer, and the ratio of stiffness of the upper layer to the stiffness of

the lower layer, on pile response. However, these analyses are based on simplified

assumptions and do not consider the non-linearity of soil, which is one of the main

advantages of the p-y approach.

Georgiadis (1983) proposed a new approach to develop p-y curves in a layered

soil system. The soil layering is taken into account by computing equivalent depths for

each of the underlying layers. The determination is presented schematically in Figure

2.19. The p-y curves of the first soil layer are determined according to the standard

criteria for homogeneous soils. To compute the p-y curves of the second layer, the

equivalent depth h2 of the top of this layer has to be previously determined. The force F1

required to induce the soil failure of the pile segment embedded to the bottom of the

upper layer is computed by performing an integration of the ultimate resistance, pu1, of

the p-y curves, over the thickness, H1, of the first layer as:.

∫=1

011

H

u dHpF (2.8)

The embedded depth, h2, of the same pile in a material having the properties of

the second layer is calculated so that the force required to cause failure is equal to F1.

This depth is the equivalent depth of the top of the second layer and is obtained from the

solution of the following equation:

27

∫=2

021

h

u dHpF (2.9)

where the pu2 is the ultimate soil resistance of the p-y curves which is a function of the

equivalent depth, the actual overburden pressure and the strength properties of the second

layer. When the equivalent depth of the top of the second layer has been determined the

p-y curves of this layer can be computed using the conventional p-y criteria. The

equivalent depth h3 and the p-y curves of the third layer are obtained by the same

procedure.

The lateral pile response predicted using this new approach and the homogeneous

soil p-y approach for layered soil were compared to field test results obtained from the

literature. Excellent agreement was found between the field test results and those

predicted by the new method in terms of both maximum bending moment and deflection.

The pile response computed by the homogeneous soil properties throughout the entire

depth, was found to either overestimate or underestimate the actual pile capacity with

respect to the equivalent depth method and the field test results, depending on whether

the upper layer is softer or stiffer than the underlying layer, respectively.

2.2.5 Other Methods

Besides the methods in analyzing the lateral pile behavior mentioned earlier,

several other methods which cannot be categorized into the previous groups, have been

summarized in the following sections.

2.2.5.1 Equivalent Cantilever Approach

A common method that structural engineers and the California Department of

Transportation (Caltrans) often use to analyze the responses of laterally loaded piles is

the equivalent cantilever method. In this method, the soil-pile system is replaced by an

28

equivalent cantilever fully restrained against translation and rotational at the base without

surrounding soil as presented in Figure 2.20. The equivalent depth of fixity can be

determined by equating the lateral stiffness of the soil-pile system to that of an equivalent

fixed-base cantilever. The depth of fixity can be determined by trial and error until the

equivalent system has the same displacement with the actual soil-pile system. Design

charts based on this concept were developed to facilitate the design engineer to determine

the depth of fixity for various soil types as presented in Figure 2.21.

In this method, the displacement ductility of the pile can be estimated as presented

below (Budek, 1997).

The yield displacement can be determined as

3)( 2

fayy

LL +=∆

φ (2.10)

where La = above-ground height, Lf = equivalent depth of fixity, φy = yield curvature.

The plastic rotation θp is given by

( )yupp L φφθ −= (2.11)

where Lp = plastic hinge length, and φu = ultimate curvature.

The plastic displacement at the top of the pile can be written as:

)( mapp LL +=∆ θ (2.12)

where Lm = depth to maximum moment.

29

The displacement ductility of the pile can be then determined by

y

p

y

u

∆

∆+=

∆∆

=∆ 1µ (2.13)

The drawback of this method is that the depth to fixity is determined based on

solutions for an elastic pile embedded in elastic soil. This assumption is not appropriate

because the behavior of most soils is highly nonlinear. Second, the depth of maximum

moment does not occur at the base of the cantilever but at a depth shallower than the

equivalent depth to fixity. Third, current design practices usually assume that the depth

of maximum moment occurs approximately 2D below the ground surface with a plastic

hinge length is equal to the pile diameter D. This value is based on intuition, without any

test evidence or theoretical basis.

Chai and Hutchinson (1999) showed that the depth to maximum moment can be

determined by assuming the ultimate soil pressure mobilized by the pile. The plastic

hinge length based on the experimental test results of 4 reinforced concrete piles with two

different above-ground heights showed that the plastic hinge length was about 1.2D for

the piles with an above ground height of 2D and 1.6D for those with an above ground

height of 6D.

2.2.5.2 Strain Wedge Approach

Ashour and Norris (1998 and 2000) developed the new approach using a Strain

Wedge (SW) model to predict the response of a flexible pile under the lateral loading.

The strain wedge model parameters are related to a three-dimensional passive wedge of

soil developing in front of the pile as presented in Figure 2.22. The basic purpose of the

SW model is to relate stress-strain-strength behavior of the soil in the wedge using a

Mohr-Coulomb representation of soil strength to the one dimensional beam on elastic

30

foundation parameters (BEF). Therefore, the response of the pile under lateral loading

can be obtained by solving the fourth order differential equation (Eq. 2.3) with the BEF

parameters.

The concept of the strain wedge method is that as the pile deflects, a growing

passive wedge develops in front of the pile. The SW model is characterized by base

angles Θm and βm , the current passive depth, h, and the spread of the wedge fan angle, ϕm

(mobilized friction angle). The soil resistance consists of the horizontal stress change at

the passive wedge face, ∆σh, and the side shear, τ , as shown in Figure 2.22a. It is

assumed that the deflection pattern of the pile is taken to be linear over the controlling

depth of the soil near the pile top, resulting in a linearized deflection angle, δ, as

presented in Figure 2.22b. Changes in the shape and depth of the passive wedge, together

with changes in the state of loading and pile deflection, occur with the change in the

uniform strain in the developing passive wedge.

An iterative procedure is used to evaluate h and Θm under a given head load. As

part of this procedure, at each point along the deflected pile, horizontal soil strain in front

of the pile is related to stress level, SL. The horizontal stress, ∆σh, is used to evaluate a

passive resultant force, which when combined with a side shear force, yields quantity p in

the p-y curve. Quantity y is readily determined from strain, ε, and Θm. Therefore, by

varying the pile head load, the corresponding nonlinear p-y curves can be obtained. The

application of this method in the problem of multiple soil layers is also possible as

presented in Figure 2.23.

The p-y curves developed based on this concept show that they are not unique and

change not only with soil properties, but also with the pile properties such as the pile

stiffness, pile diameter, pile head fixity, and cross section. This is significantly different

from the standard p-y curves, where the p-y curves are dependent on only the soil

properties and pile diameter.

31

2.3 Full-Scale Pile Testing on Single Piles

Numerous full-scale lateral pile load tests (Table 2.14) have been conducted to

understand the behavior of soil-structure interaction, varying from small diameter timber

and steel pipe piles to large diameter cast-in-place shafts. The tests include static and

cyclic loading in various types of soil. The tests were conducted by using the hydraulic

jack or actuator to provide the applied force to the pile head. The displacement of the

pile was measured using displacement transducers. Some of the tested piles were also

instrumented with strain gauges to measure the moment along the pile and thus allow to

back-calculated the p-y curves. For instrumented piles where moment data is available,

the data were used to back-calculate the p-y curves. The method in constructing the p-y

curves for different soil types have been proposed as mentioned earlier. As can be seen

from Table 2.14, these p-y curves were developed based on the limited number of the

tests, and then they were extrapolated for use with different soil strengths, and other pile

diameters. As a result, the verification of these p-y curves using further full-scale testing

results is still necessary. Some of lateral load tests in the literature were conducted to

compare the measured responses with the results from analyses using the available

methods for estimating the pile responses, such as elastic continuum, subgrade reaction

theory, and p-y curve methods. Brief descriptions on some of these full-scale lateral tests

are discussed below.

Weaver (2001) and Ashford and Rollins (2002) conducted full-scale lateral load

tests in liquefied soil using controlled-blast technique at Treasure Island. The p-y curves

of liquefied soil at various excess pore pressure ratios were back-calculated based on the

results of instrumented piles. They found that the characteristic shape of the liquefied p-y

curves is dramatically different from standard p-y curves with the shape of the p-y curves

being concave up. The soil resistance increased as the excess pore water ratios decreased.

Furthermore, the pile diameter has an effect on the p-y curves in liquefied soil with the

soil resistance being increased with the pile diameter.

32

Jayonan et al. (2001) conducted field testing on an extensively instrumented large

diameter CIDH shaft/column (1.8 m in diameter) at a stiff clay site and developed the p-y

curves from section curvature measurements using the bilinear moment-curvature

relationship. He stated that using the nonlinear moment-curvature relationship is an

important feature of the results, as previous data reduction routines, by using linear

moment-curvature relations, have lumped both shaft and soil nonlinearity into p-y curves.

The finding of this study indicates that the actual p-y response near the ground surface is

considerably stiffer than that predicted by existing models. Use of existing models would

result in an underprediction of the failure load for the column and an overprediction of

the plastic hinge depth relative to what was measured during the test.

Chai and Hutchinson (1999) investigated inelastic behavior of reinforced concrete

piles in loose and dense dry sand with above ground height of 6D and 2D under cyclic

lateral loading. A total of four 406 mm diameter reinforced concrete piles with a

longitudinal steel of 2.1% and a confining steel ratio of 0.57 and 1.06% were used in test

piles. The test piles were constructed as precast units and positioned in a container before

the placement of soil. Then the soil was filled and compacted layer by layer using

vibratory flat-plate compactor to achieve required soil density by controlling the layer

thickness of each lift, number of pass per lift, and amount of input energy from the

compactor. The test piles were instrumented with electrical resistance strain gauges

along 4 longitudinal steel bars and four principal directions of spiral, curvature rods with

linear potentiometer, and inclinometers. The load cell in the actuator, together with linear

potentiometers at the pile head, were used to obtain load-displacement characteristics as

well as pile head rotations. The test results showed that all four test piles exhibited a

ductile behavior even though fairly low transverse reinforcement ratio of about ½ of that

required by the Applied Technology Council (ATC-32) was used. Surprisingly, test

results indicated that the maximum lateral force of the soil-pile system was not sensitive

to the soil density. However, the depth of maximum moment appeared to decrease with

an increase in soil density and an increase in the above ground height. Furthermore, the

33

kinematic model based on the equivalent fixed base cantilever concept was proposed to

simulate the curvature ductility demand. The model was shown to provide a reasonable

prediction of ductility demand upon yielding of the pile. No p-y curves were developed

in this study.

Some of the other main findings observed from other lateral pile load tests listed

in Table 2.14 are summarized as the following:

1. Vertical pile can provide some resistance against lateral loading.

2. The lateral pile response is dominated by the soil at shallow depth. If the pile

length is longer than an effective length, there is no change on the pile

response.

3. Cyclic loading causes an increase in total deflection. The first cycle causes

significant more cyclic degradation than during the next other cycles. After a

large number of cycles of loading, a soil pile system tends to be stabilized.

4. Load displacement curve of laterally loaded pile appears to be highly

nonlinear due to the effect of soil nonlinearity.

5. The characteristic of p-y curves are highly nonlinear, inelastic, and dependent

on the soil type.

6. The p-y curve characteristics appear to be independent of pile-head restraint.

(Matlock, 1970).

Though many full-scale testing have been conducted to study the behavior of

laterally loaded pile, some important issues have not been yet resolved. These include

the effect of pile installation, the behavior of pile in cemented sand, the effect of pile

diameter on p-y curves, and application of p-y curves for rigid piles. For this reason,

further full-scale testing is still needed to provide further insight into behavior of soil-pile

interaction and resolve these problems.

34

2.4 Inelastic Behavior of Concrete Piles

For most bridges, the foundation systems are usually designed to remain elastic

during an earthquake. However, in many cases the plastic hinging in the members of the

foundations system cannot be avoided during severe earthquakes (e.g., using integral pile

shaft-column). Research has been conducted to study the inelastic behavior of piles

(i.e., Ikeda et al., 1982; Banerjee et al., 1987; Falconer and Park, 1982; Pam et al., 1988;

and Muguruma et al., 1987). However, all of these tests were performed on prestressed

concrete piles in the laboratory without the soil. Recent research by Budek (1997)

showed that external confinement, such as from soil, plays a very significant role in pile

shaft response. Budek performed the load test on piles by using a group of neoprene-

lined saddles extending 100o around the circumference of shaft, top and bottom, to

simulate the lateral confinement by soil. Figure 2.24 presents a comparison of load-

displacement curves of the piles with and without the effect of external confinement. It

shows that the confining pressure provided by the external confinement can significantly

increase the effective confinement on the section and retard localized plastic rotation and

that only moderate levels of transverse reinforcement are needed for adequate seismic

performance.

2.5 Typical Behavior of Cemented Soil

In this research, the full-scale lateral loaded pile tests were conducted in weakly

cemented soil. A review of a typical behavior of cemented soil is summarized in the

following paragraphs.

Cemented soils are found in many areas in the world. Examples include marine

terrace deposits along the Pacific coast of the United States, loess deposits in the mid-

west United States and China, and volcanic ash deposits in Japan and Guatemala (Sitar,

1990). Cemented sands are characterized by their ability to stand in very steep natural

slopes. The common cementing agents are silica, clays, carbonates, and iron oxides. It

35

seems that the relatively undisturbed samples of this soil types for laboratory testing is

very difficult, and that conventional geotechnical design would usually tend to be

conservative and neglect the presence of cementation.

Saxena and Lastrico (1978) studied the behavior of lightly cemented sand under

static loading. They found that the at low strain level the soil strength from the cohesion

component was predominant whereas the strength from friction component governed the

soil behavior at the high strain levels.

Clough et al. (1981) investigated behavior of cemented soils to use in a study of

investigation of slope behavior in cemented soils. A total of 137 laboratory tests were

performed on four samples of naturally occurring cemented soils and on artificially

cemented soils fabricated to simulate the natural soil behavior. The artificially cemented

soils were used because it is difficult to obtain undisturbed specimens of the sensitive

natural slope. Furthermore, the artificially cemented soils allow evaluating the effects of

amount of cementing agent and sand density on soil response. The artificially cemented

soils were prepared by mixing Type II Portland cement and a uniform sand together with

a water content of 8%. It was found from basic properties of four naturally cemented

soils that the more well-cemented soils have a significant fraction of fines. The

laboratory tests consisted of drained triaxial compression, Brazilian, and simple shear

tests. The tests results of naturally cemented soil indicated that the stiffness and peak

strength increases with increasing of confining stress. The strongly cemented soil

showed the brittle failure behavior at all confinements, while the moderate and weakly

cemented soil showed a transitional response from brittle failure to ductile failure as

confining pressures increase as presented in Figure 2.25. The volumetric strain increases

during shearing, however decreases as confining pressure increases. Although Clough et

al. concluded that the initial modulus of cemented soil increases with increasing

confining pressure, it seemed that the stiffness of initial slope is independent of confining

36

pressure as presented in Figure 2.25c and Figure 2.25d. Based on the artificially

cemented soil test results, the following conclusion can be drawn.

1. The peak strength increases with degree of cementation.

2. The strain at peak strength mobilization decreases with degree of cementation.

3. The volumetric strain increase during shear is concentrated over a small strain

range and occurs at a lower strain as degree of cementation increases.

4. The residual strength of cemented sand is close to that of uncemented sand.

37

Table 2.1 Summary of Elastic Solutions for Laterally Loaded Pile for the Case of Constant Soil Modulus with Depth (after Poulos, 1971)

Pile Response Free-Head Pile Fixed-Head Pile

Pile Head Displacement ( u ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛= 2LE

MILE

HIus

UMs

UH

⎟⎟⎠

⎞⎜⎜⎝

⎛=

LEHIu

sUF

Pile Head Rotation (θ ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛= 3LE

MILE

HIs

Ms

H θθθ 0

Maximum Moment (Mz)max for Free-Head Pile or Fixing Moment at Pile Head (Mf) for Fixed-Head Pile

From Figure 2.1 From Figure 2.1

Note:

4LEIE

Ks

ppR =

where: D = Pile diameter

Ep = Modulus of elasticity of pile Es = Soil modulus H = Applied horizontal force at ground level Ip = Moment of inertia of pile IUH, IUM, IθH, IθM, IUF = Dimensionless Elastic influence factors

(from Figure 2.1) KR = Pile flexibility factor, L = Pile length M = Moment at ground level νs = Poisson’s ratio

38

Table 2.2 Summary of Elastic Solutions for Laterally Loaded Pile for the Case of Constant Soil Modulus with Depth (after Davies and Budhu, 1986) Pile Response Free-Head Pile Fixed-Head Pile

Pile Head Displacement (u)

2DEMI

DEHIu

sUM

sUH +=

where 11/23.1 −= KIUH

11/22.2 −== KII HUM θ

DEHIus

FH=

where 11/280.0 −= KI FH

Pile Head Rotation (θ) 32 DE

MIDE

HIs

Ms

H θθθ +=

where 11/82.9 −= KI Mθ

0

Maximum Moment (MM) for Free-Head Pile or Fixing Moment at Pile Head (MF) for Fixed-Head Pile

HDIM MHM =

where 11/312.0 KI MH =

HDIM MFF −=

where 11/324.0 KI MF =

Location of Maximum Moment (LM)

11/420.0 DKLM = --

Note:

sp EEK /=

where: D = Pile diameter Ep = Modulus of elasticity of pile Es = Soil modulus H = Applied horizontal force at ground level IUH, IUM, IθH, IθM, IMH, IMF = Compliance factor K = Pile stiffness ratio L = Pile length M = Moment at ground level

39

Table 2.3 Summary of Elastic Solutions for Laterally Loaded Pile for the Case of Linearly Increasing Soil Modulus with Depth (after Budhu and Davies, 1988) Pile Response Free-Head Pile Fixed-Head Pile

Pile Head Displacement (u)

32 mDMI

mDHIu UMUH +=

where 9/32.3 −= KIUH

9/50.5 −== KII HUM θ

2mDHIu FH=

where 9/34.1 −= KI FH

Pile Head Rotation (θ) 43 mD

MImD

HI MH θθθ +=

where 9/76.13 −= KI Mθ

0

Maximum Moment (MM) for Free-Head Pile or Fixing Moment at Pile Head (MF) for Fixed-Head Pile

HDIM MHM =

where 9/23.0 KI MH=

HDIM MFF −=

where 9/24.0 KI MF =

Location of Maximum Moment (LM)

9/253.0 DKLM = --

Note:

mDEK p /= mzEs =

where: D = Pile diameter Ep = Modulus of elasticity of pile Es = Soil modulus H = Applied horizontal force at ground level IUH, IUM, IθH, IθM, IMH, IMF = Compliance factor K = Pile stiffness ratio L = Pile length m = Constant (Rate of increasing soil modulus with depth) M = Moment at ground level

40

Table 2.4 Summary of Definition and Dimension of Terms Used in Analysis of Laterally Loaded Piles

Description Symbol Definition Dimension

Soil resistance per unit length p F/ L

Pile deflection y L

Pile diameter D L

Spring spacing ∆L L

Spring force F F = p*∆L F

Soil pressure P P = p/D F/ L2

Modulus of subgrade reaction K K = p/y F/ L2

Soil spring stiffness Ks Ks = F/y, Ks = K*∆L F/ L

Coefficient of subgrade reaction k k = P/y, k = K/D F/ L3

41

Table 2.5 Summary of Solutions for Laterally Loaded Pile due to Horizontal Loading for the Case of Constant Subgrade Reaction (Hetenyi, 1946) Pile

Response Due to Horizontal Loading, H

Pile Displacement (u)

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−−−⎟⎟⎠

⎞⎜⎜⎝

⎛=

LLzLLzLzL

DkHuh ββ

ββββββ22 sinsinh

)(coshsin)(coshcossinh2

Pile Rotation (θ)

( ) ( )[ ]( ) ( )[ ]⎟⎟⎠

⎞⎜⎜⎝

⎛−+−+

−+−

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛=

zLzzLzLzLzzLzL

LLDkH

h

ββββββββββ

βββθ

sincoshcossinhsinsinhcoscoshsinsinh

sinsinh12

22

2

Shear Force (Q) ( ) ( )[ ]

( ) ( )[ ]⎟⎟⎠⎞

⎜⎜⎝

⎛−−−−−−−

⎟⎟⎠

⎞⎜⎜⎝

⎛−

Η−=

zLzzLzLzLzzLzL

LLQ


ββ

cossinhsincoshsincoshsinsinhcossinh

sinsinh 22

Moment (M) ( ) ( )

⎥⎦

⎤⎢⎣

⎡−

−−−⎟⎟⎠

⎞⎜⎜⎝

⎛ Η−=

LLzLzLzLzLM

ββββββββ

β 22 sinsinhsinsinhsinsinhsinsinh

where : 4/1

4 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

pp

h

IEDk

β

D = Pile Diameter EpIp = Pile Stiffness kh = Coefficient of Subgrade Reaction

z = Depth

42

Table 2.6 Summary of Solutions for Laterally Loaded Pile due to Moment Loading for the Case of Constant Subgrade Reaction (Hetenyi, 1946)

Pile Response

Due to Moment Loading, Mo

Pile Displacement (u)

( ) ( )[ ]( ) ( )[ ]⎟⎟⎠

⎞⎜⎜⎝

⎛−−−+

−−−

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=

LzzzLzLzzLzzLL

LLDkM

uh


βββ

sincoshcossinhsincossinhsincoshsinh

sinsinh12

22

20

Pile Rotation (θ) ( ) ( )

⎥⎦

⎤⎢⎣

⎡−

−+−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

LLzLzLzzLL

DkM

h

ββββββββ

βθ

22

30

sinsinhcoscoshsincoscoshsinh

4

Shear Force (Q)

( )( )

( )( ) ⎟

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎥⎦

⎤⎢⎣

⎡−

+−−

⎥⎦

⎤⎢⎣

⎡−

+−

−=

zLzzLz

L

zzLzzL

L

LLM

M

ββββ

β

ββββ

β

ββsincoshcossinh

sin

sincoshcossinh

sinh

sinsinh 220

Moment (M) ( )

( ) ⎥⎦

⎤⎢⎣

⎡−

+−

−−

=zLzLzzLL

LLM

Qβββ

βββββ

βsinsinhsin

sinsinsinsinsinh

222

0

where : 4/1

4 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

pp

h

IEDk

β

D = Pile Diameter EpIp = Pile Stiffness

kh = Coefficient of Subgrade Reaction z = Depth

43

Table 2.7 Summary of Procedure in Developing Soft Clay p-y Curves (Matlock, 1970) Static Loading 1. Compute Ultimate Soil Resistance, pu (Using the smaller values)

DczDJz

cp u

uu ⎥

⎦

⎤⎢⎣

⎡++=

'3 γ

Dcp uu 9= 2. Compute Deflection at One-Half the Ultimate Soil Resistance, y50

Dy 5050 5.2 ε=

3. Develop p-y Curves using the following Expression

31

50

5.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

yy

ppult

Cyclic Loading 1. Develop p-y Curves Construct p-y curves in the same manner as for static

loading for values of p less than 0.72 pu 2. Determine Transition Depth, zr )'(

6

u

ur JcD

Dcz

+=

γ

3.If the depth is greater than or equal zr

upp 72.0= for y >3y50

4. If the depth is less than zr ultpp 72.0= at y = 3y50 and

⎟⎟⎠

⎞⎜⎜⎝

⎛=

rult z

zpp 72.0 at y = 15y50

where: cu = Undrained Shear Strength

D = Pile Diameter J = Constant (0.5 for Soft Clay and 0.25 for Medium Clay) pu = Ultimate Soil Resistance

y50 = Deflection at One-Haft the Ultimate Soil Resistance z = Depth

zr = Transition Depth γ’ = Effective Soil Unit Weight ε50 = Strain at One-Haft the Ultimate Soil Resistance 0.020 for soft clay, 0.010 for medium clay, and 0.005 for stiff clay

44

Table 2.8 Summary of Procedure in Developing Stiff Clay with Free Water p-y Curves (Reese et al., 1975) Static Loading 1. Compute Ultimate Soil Resistance, pu (Using the smaller values)

zcDzDcp aatu 83.2'2 ++= γ (Wedge Failure) Dcp uud 11= (Flow Failure)

2. Establish Initial Straight Line Portion

yzkp s )(= for Static, yzkp c )(= for Cyclic


5.0

50

5.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

yypp u , Dy 5050 ε=

4. Develop the Second Parabolic Portion of the p-y Curves (from Asy50 to 6Asy50)

25.1

50

50

5.0

50

055.05.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛ −−⎟⎟

⎠

⎞⎜⎜⎝

⎛=

yAyAy

pyypp

s

suu

5. Establish Straight-Line Portion (from 6Asy50 to 18Asy50)

)6(0625.0411.0)6(5.0 5050

5.0 yAypy

pApp suusu −−−=

6. Establish Final Straight-Line Portion (beyond 18Asy50)

suusu AppApp 75.0411.0)6(5.0 5.0 −−=

Cyclic Loading 1. Follow Step 1 to 3 of Static Case

Follow Step 1 to 3 of Static Case

2. Establish Parabolic Portion (up to 0.6 yp)

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡ −−=

5.2

45.045.0

1p

puc y

yypAp , 501.4 yAy cp =

3. Establish Straight-Line Portion (from 0.6yp to 1.8yp) )6.0(085.0936.0

50puuc yyp

ypAp −−=

4. Establish Final Straight-Line Portion (beyond 1.8Asy50 puuc yp

ypAp

50

102.0936.0 −=

where: As, Ac = Constants (from Figure 2.7c)

ca = Average Undrained Shear Strength over Depth z cu = Undrained Shear Strength D = Pile Diameter ks, kc = Initial Subgrade Reaction Constant for Static and Cyclic Loading

y50 = Deflection at One-Haft the Ultimate Soil Resistance z = Depth

ε50 = Strain at One-Haft the Ultimate Soil Resistance (0.004-0.007) γ’ = Effective Soil Unit Weight

45

Table 2.9 Summary of Procedure in Developing Stiff Clay with No Free Water p-y Curves (Welch and Reese, 1972;and Reese and Welch, 1975) Static Loading 1. Compute Ultimate Soil Resistance, pu (Using the smaller values)

DczDJz

cp u

uu ⎥

⎦

⎤⎢⎣

⎡++=

'3 γ

Dcp uu 9= 2. Compute Deflection at One-Half the Ultimate Soil Resistance, y50

Dy 5050 5.2 ε=


41

50

5.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

yy

pp

u

for y<16y50

upp = for y>16y50 Cyclic Loading 1. Develop p-y Curves for Static Loading

Follow Step 1 to 3

2. Determine Parameter Describing Effect of Repeated Loading, C

4

6.9 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

uppC

3. Determine y for Cyclic Loading , yc

NCyyy sc log50+=

where: cu = Undrained Shear Strength D = Pile Diameter

J = Constant = 0.5 N = Number of Cycles pult = Ultimate Soil Resistance y50 = Deflection at One-Haft the Ultimate Soil Resistance yc = Deflection under N-Cycles of Load ys = Deflection under Short-Term Static z = Depth ε50 = Strain at One-Haft the Ultimate Soil Resistance 0.020 for soft clay, 0.010 for medium clay, and 0.005 for stiff clay γ’ = Effective Soil Unit Weight

46

Table 2.10 Summary of Procedure in Developing Sand p-y Curves (Reese et al., 1974)

1. Preliminary Computation

2φα = ,

245 φβ += , 4.00 =K , ⎟

⎠⎞

⎜⎝⎛ −=

245tan 2 φ

aK

2. Theoretical Ultimate Soil Resistance due to Wedge Failure, pst ( ) ( ) ( )

( ) ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−+

+−

+−=

DKzK

zDzK

zp

a

st

αβφβ

αβφβ

βαφββφ

γtansintantan

tantantan

tancostansintan

'

0

0

3. Theoretical Ultimate Soil Resistance due to Flow Failure, psd

( ) βφγβγ 40

8 tantan'1tan' zDKzDKp asd +−=

4. Govern Theoretical Ultimate Soil Resistance, ps

ps = the smaller of the values given from step 2 and 3

5. Ultimate Soil Resistance, pu ssu pAp = for static loading or scu pAp = for cyclic loading

6. Soil Pressure at D/60 ssm pBp = for static loading or scm pBp = for cyclic loading


( )ykzp =

8. Establish Parabolic Section of p-y Curves nyCp 1

= , mu

mu

yypp

m−−

= , m

m

mypn = ,

nm

m

ypC 1= ,

1−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

nn

kzCyk

where: sA , cA = Adjustment Coefficient for Static and Cyclic p-y Curves from

Figure 2.9a Bs, Bc = Nondimensional Coefficient for Static and Cyclic p-y Curves from

Figure 2.9b D = Pile Diameter k = Initial Subgrade Reaction Constant (MN/m3) Loose Sand (Submerge/above water) 5.4/ 6.8 Medium Dense Sand 16.3/ 24.4 Dense Sand 34/ 61 psd = Theoretical Ultimate Soil Resistance due to Flow Failure pst = Theoretical Ultimate Soil Resistance due to Wedge Failure ps = Govern Ultimate Soil Resistance pu = Ultimate Soil Resistance z = Depth φ = Friction Angle

γ’ = Effective Soil Unit Weight for Soil under Water

47

Table 2.11 Summary of Procedure in Developing API Sand p-y Curves (API, 1987) 1. Theoretical Ultimate Soil Resistance due to Wedge Failure, pst

( ) zDCzCpst '21 γ+=

2. Theoretical Ultimate Soil Resistance due to Flow Failure, psd

zDCpsd '3 γ=

3. Govern Theoretical Ultimate Soil Resistance, ps

ps = the smaller of the values given from step 2 and 3

4. Determine Adjustment Coefficient for Static and Cyclic Loading

9.08.00.3 ≥⎟⎠⎞

⎜⎝⎛ −=

DzAs for static lading

9.0=cA for cyclic loading

5. Develop Characteristic Shape of p-y Curves ⎟

⎟⎠

⎞⎜⎜⎝

⎛= y

pAkzpAp

us tanh

where: sA , cA = Adjustment Coefficient for Static and Cyclic p-y Curves

C1, C2, C3 = Coefficients from Figure 2.12a D = Pile Diameter

k = Initial Subgrade Reaction Constant (MN/m3) from Figure 2.12b psd = Theoretical Ultimate Soil Resistance due to Flow Failure pst = Theoretical Ultimate Soil Resistance due to Wedge Failure ps = Govern Ultimate Soil Resistance pu = Ultimate Soil Resistance z = Depth φ = Friction Angle

γ’ = Effective Soil Unit Weight for Soil under Water

48

Table 2.12 Summary of Procedure in Developing Cemented Sand p-y Curves (Ismael, 1990) 1. Ultimate Soil Resistance, pu

DCp ppu σ=

2. Correction Factor, Cp

Cp = 1.5 for ≤φ 15o

Cp = 10φ for >φ 15o

3. Passive Earth Pressure, σp ⎟

⎠⎞

⎜⎝⎛ ++⎟

⎠⎞

⎜⎝⎛ +=

245tan

245tan2 2 φσφσ vp c

4. Characteristic Shape of p-y Curves

3/1

50

5.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

yy

pp

u

5. Pile Deflection at which p = 0.5pu, y50

Dy cε5.250 =

where: c = Soil Cohesion

Cp = Correction Factor for Small Width of Pile D = Pile Diameter pu = Ultimate Soil Resistance y50 = Pile Deflection at p = 0.5pu φ = Soil Friction Angle σp = Passive Earth Pressure σv = Effective Vertical Stress εc = Strain at (σ1-σ3) = 0.5(σ1-σ3)u (σ1-σ3)u = Ultimate Principal Stress Difference in Triaxial Test σ1 = Major Principal Stress σ3 = Minor Principal Stress

49

Table 2.13 Summary of Procedure in Developing Silt p-y Curves (Reese and Van Impe, 2001) 1. Preliminary Computation 2

φα = , 2

45 φβ += , 4.00 =K , ⎟⎠⎞

⎜⎝⎛ −=

245tan 2 φ

aK

2. Ultimate Soil Resistance, pu

ucusu ppAp += φ for Static

ultcultcult ppAp += φ for Cyclic 2. Friction Component, puφ

(The smaller values from these 2 Eqs.)

[ ]DKzKz

zDK

zp

ao

ou

−−+

⎥⎦

⎤⎢⎣

⎡+

−+

−=

)tansin(tantan

)tantan()tan(

tancos)tan(

sintan'

αβφβγ

αβφβ

βαφβ

βφγφ

βφγβγφ

48 tantan')1(tan' zDKzDKp oau +−= 3. Cohesion Component, puc

(The smaller values from these 2 Eqs.)

cDzDJz

cpuc ⎟

⎠⎞

⎜⎝⎛ ++=

'3 γ

cDpuc 9=

4. Soil Pressure at D/60

ssm pBp = for Static Loading or scm pBp = for Cyclic Loading


( )yzkp py= , φkkk cpy += kc from Figure 2.15b

6. Establish Parabolic Section of p-y Curves

nyCp 1= ,

mu

mu

yypp

m−−

= , m

m

mypn = ,

nm

m

ypC 1= ,

1−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

nn

zkCypy

k

where: c = Soil Cohesion

D = Pile Diameter J = Constant kc, kf = Initial Subgrade Reaction Constant from Cohesion and Friction

Components, Respectively (from Figure 2.15) ps = Govern Ultimate Soil Resistance (from Step 4 of Table 2.4) kpy = Initial Subgrade Reaction Constant pu = Ultimate Soil Resistance pφ = Ultimate Soil Resistance from Friction Component pc = Ultimate Soil Resistance from Cohesion Component z = Depth φ = Friction Angle γ’ = Effective Soil Unit Weight

50

Tab

le 2

.14

Sum

mar

y of

Cas

e H

isto

ries o

f Lat

eral

ly L

oade

d Si

ngle

Pile

s

51

D

UH

D

UM

D

D

D

Figure 2.1 Influence Factors for Determination of Lateral Pile Responses for the Case of Constant Soil Modulus (after Poulos, 1971)

52

V M VM

Prototype Idealized using Winkler Spring Method

Figure 2.2 Implementation of Winkler Spring Concept for Laterally Loaded Pile Problem

a) Pile at Rest b) Pile after Load Applied

Figure 2.3 Definition of p-y Concept with a) Pile at Rest; b) Pile after Load Applied (after Dunnavant, 1986)

53

Figure 2.4 Typical Family of p-y Curves Response to Lateral Loading (after Dunnavant, 1986)

MH

Deflection Rotation Moment Shear Soil Resistance

y S = dy/dx M=EI(d2y/dx2) V=EI(d3y/dx3) p=EI(d4y/dx4)

Figure 2.5 Methodology in Developing p-y Curves (Reese and Van Impe, 2001)

54

z>zr

For z<zr

z/zr

Static Loading

Cyclic Loading

Figure 2.6 Characteristic Shape of p-y Curve for Soft Clay a) Static Loading; b) Cyclic Loading (after Matlock, 1970)

55

U

U

U

D

Z

U

a) Static Loading

U

U

U

DZ

b) Cyclic Loading

Z/D

c) Value of Constant A

Figure 2.7 Characteristic Shape of p-y Curve for Stiff Clay below Water Table for a) Static Loading; b) Cyclic Loading; c) Value of Constant A (after Reese et al., 1975)

56

a) Static Loading

b) Cyclic Loading

Figure 2.8 Characteristic Shape of p-y Curve for Stiff Clay above Water Table for a) Static Loading; b) Cyclic Loading (Welch and Reese 1972; Reese and Welch, 1975)

57

Z = Z1

Z = Z2

Z = Z3

Z = Z4

Z = 0

D/60 3D/80Z

Figure 2.9 Characteristic Shapes of p-y Curves for Sand (Reese et al., 1974)

D

a) Assumed Passive Wedge Failure b) Assumed Lateral Flow Failure

Figure 2.10 Sand Failure Modes in Laterally Loaded Pile Problem a) Assumed Passive Wedge Failure; b) Assumed Lateral Flow Failure (after Reese et al., 1974)

60

a) Values of kc

b) Values of kφ

Figure 2.15 Initial Subgrade Reaction Constant (Reese and Van Impe, 2001) a) Values of kc, and b) Values of kφ

Deflection (y )

Soil

Pres

sure

(P)

Increasing n

P ult

k o

Figure 2.16 Hyperbolic Soil Model (after Carter, 1984)

58

a) Coefficient A

b) Coefficient B

Figure 2.11 Values of Coefficients Used for Developing p-y Curves for Sand a) Coefficient A; b) Coefficient B (after Reese et al., 1974)

a) Coefficients as Function of φ for API Sand

b) Initial Modulus of Subgrade Reaction for API Sand

Figure 2.12 Charts Used for Developing API Sand p-y Curves (API, 1987)

59

y/y50

p/p u

8.0

p/pu = 0.5(y/y50)1/3

1.0

0.5

1.0

pu =CpσpDσp = 2ctan(45+φ/2)+σvtan2(45+φ/2)

Figure 2.13 Characteristic Shape of p-y Curve for Cemented Sand (after Ismael, 1990)

D/60 3D/80

Figure 2.14 Characteristic Shape of p-y Curve for c-φ Soil (Reese and Van Impe, 2001)

61

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 0.5 1 1.5 2

Pile Diameter (m)

Rat

io o

f Pre

dict

ed to

Mea

sure

d D

efle

ctio

n

TerzaghiLing

Figure 2.17 Comparison of Ratio of Predicted to Measured Pile Head Deflections based on Two Different Concepts on Pile Diameter Effect (After Ling, 1988)

Figure 2.18 Influence of Pile Diameters on Dimensions of Bulb Pressure (Terzaghi, 1955)

62

Figure 2.19 Typical Determination of Equivalent Depths in a Layered Soil Profile (Georgiadis, 1983)

63

Figure 2.20 Concept of Equivalent Cantilever Beam Method (Chai and Hutchinson, 1999)

Figure 2.21 Design Chart for Determining Depth of Fixity (Budek, 1997)

64

Figure 2.22 Concept of Strain Wedge Model for Analyzing Lateral Load Pile Problem (Ashour and Norris, 1998)

Figure 2.23 Distribution of Soil-Pile Reaction along Deflected Pile (Ashour and Norris, 1998)

65

a) without External Confinement

b) with External Confinement

Figure 2.24 Force-Displacement Hysteretic Loops for Pile Shaft Test a) without External Confinement, b) with External Confinement (Budek, 1997)

66

a) Strongly Cemented Sand (from Natural Soil Samples)

b) Weakly Cemented Sand (from Natural Soil Samples)

c) Artificially-Cemented Sand (4% Cement)

d) Artificially-Cemented Sand (2% Cement)

Figure 2.25 Typical Stress-Strain Curves for Cemented Sand (After Clough et al., 1981); a) Strongly Cemented, b) Weakly Cemented, c) Artificially-Cemented (4% Cement), d) Artificially-Cemented (2% Cement)

67

Chapter 3 EVALUATION OF PILE DIAMETER EFFECT USING 3-D FINITE ELEMENT METHOD

In this chapter, the effect of pile diameter on lateral pile response using the finite

element method is discussed. Since the pile diameter effect is a geometrical problem in

three-dimensional space, 3-D finite element analyses were required to complete the

objective of this study. The Finite Element Analysis Program, FEAP (Taylor 1998), was

used for this parametric study. Two models, including linear elastic and elasto-plastic

soil models, were considered in the analyses to study the variation in the effect of pile

diameter when the behavior of soil changes from linear to nonlinear. The conclusions

drawn from these tests are useful in interpreting the influence of pile diameter in the

experimental phase.

3.1 Description of Finite Element Model

The 3-D finite element method was used to study the effect of pile diameter on

pile response. The finite element mesh model for this problem is illustrated in Figure 3.1.

8-node hexahedron (brick) solid elements were used to model the soil and the pile was

modeled by using a series of beam elements. Rigid link elements were used to connect

the pile to the soil elements. The rigid links were modeled using beam elements with

very large flexural rigidity, EI, (i.e. 1,000 times the EI of the pile) such that they can

transfer the load to the soil with the plane section of the pile before and after being

subjected to the bending moment remaining plane. The advantage of symmetry was used

to decrease the number of degree-of-freedoms, thus decreasing the computational time.

In this study, the model was based upon a 0.6-m steel pipe pile with a wall thickness of

10 mm and a nominal length of 20.3 m embedded in stiff overconsolidated clay. For

each case in this study, the pile was chosen to be long enough to act as a “long pile” (i.e.,

the lateral pile response was independent of depth). The EI of the pile was computed as

1.58x105 kN-m2 and the Young’s modulus of the soil, Es, was 1.38x104 kN/m2 with

68

Poisson’s ratio of 0.45. To study the pile diameter effect on the pile response, the EI of

the pile, the pile length, as well as the Young’s modulus of the soil were kept constant

throughout the analyses, while only the pile diameter was changed. Pile diameters in this

study ranged from 0.15 m to 1.07 m, such that largest pile diameter was 7 times larger

than the smallest one. The boundary of the soil was chosen to be far enough away to

minimize boundary effects (about 20 m from the center of the pile). Roller supports were

used as a boundary condition along 4 different vertical planes, while pinned supports

were used as a boundary condition at the bottom of the mesh. In all cases, the pile was

subjected to a horizontal point load of 890 kN applied at the pile head. To check the

validity of each model, the mesh was verified by comparing the displacement at the pile

head with the solutions from the boundary element method based on elastic continuum

theory (Davies and Budhu 1986) until the error was less than 10%. These meshes were

later used for further analyses. The comparison of results based on the 3-D finite element

approach and elastic solution will be presented in the following section.

3.2 Linear Elastic Soil Model

The results of 3-D finite element analyses for different pile diameters are

presented in this section. Typical contours of horizontal stress (x-x) and horizontal

deformation in the soil mass due to the pile subjected to lateral loading are presented in

Figure 3.2. A stress concentration occurs in the soil adjacent to the pile, and the stress

becomes smaller as the distance from the pile increases. It should be noted that only

compression stress contours are presented in the figure for clarity. The same stress

pattern, but in tension, occurs on the other side due to symmetry. As the pile is subjected

to lateral load, the soil in front of the pile moves upward to form a passive wedge. Based

on the horizontal displacement contour, it can be expected that the failure plane of the

wedge is a curve as opposed to a traditional assumption that the failure plane of a wedge

is a straight line. The pile head deflection for different pile diameters using a linear

elastic soil model is presented in Figure 3.3. The results based on the solution from the

69

elastic continuum theory using the boundary element method proposed by Davies and

Budhu (1986) are in good agreement with those obtained from 3-D FEM indicating the 3-

D mesh used in these analyses is reasonably adequate to model the soil-pile interaction,

especially for the next analyses where the soil model will be changed from linear to

nonlinear.

It is clearly seen from Figure 3.3 that the pile diameter has some effect on the

response of laterally loaded pile. With the EI of the pile and stiffness of the soil being

constant, increasing the pile diameter decreases the pile head deflection. This is due to

the fact that a pile with larger diameter mobilizes more soil and hence achieves higher

lateral resistance. The pile diameter effect on moment distribution is shown in Figure

3.4a. As the pile diameter increases, the maximum moment becomes lower and the

location of maximum moment moves closer to the ground surface. The effect of pile

diameter on pile deflection profile is also shown in Figure 3.4b.

Figure 3.5 presents the relationship between normalized pile head deflection

(u/uref) and normalized pile diameter (D/Dref): where u is the pile head displacement, uref

is the reference pile head displacement (i.e., in this case the pile head displacement of the

smallest pile was used as a reference displacement), D is the pile diameter, and Dref is the

reference diameter. Figure 3.5 shows that in order to decrease the pile head displacement

two times, the pile diameter needs to be increased by approximately 10 times. For linear

elastic case, the pile diameter appears to have insignificant effect on the pile response.

The relationship between normalized pile head displacement (u/uref) and normalized pile

diameter (D/Dref) based on curve fitting is given as follows:

273.0−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

refref DD

uu

(3.1)

70

The similar relationship as shown in Eq. (3.1) can also be derived from the solutions

provided by Davies and Budhu (1986).

The input soil parameters used in the 3-D finite element analyses were Young’s

modulus and Poisson’s ratio. These parameters are not directly related to the modulus of

subgrade reaction used in the 1-D problem (i.e. Beam on Winkler’s spring problem). In

order to evaluate the effect of pile diameter on the modulus of subgrade reaction (i.e. soil

spring resistance), a pile with a series of Winkler springs was analyzed by varying the

spring stiffness. LPILE (Reese et al. 2000), a computer program for analyzing lateral

pile response using Beam on Winkler’s spring concept, was used. It was assumed that

the Beam on Winker spring method can reproduce the same response of laterally loaded

pile as the 3D-finite element without any significant error, though the Winkler method

neglects the soil continuity. Using the same pile stiffness as the previous study and

varying the soil springs until the pile head deflection matched with the deflection

obtained from the 3-D analyses for the 0.30-m pile, the moment and displacement

profiles obtained from these different types of analyses were compared, as presented in

Figure 3.6. The agreement of moment and displacement profiles obtained from the

different methods is very good, confirming that the above assumption is reasonable. The

pile head displacements with varying modulus of subgrade reaction at different EI were

then calculated as presented in Figure 3.7. The normalized pile head displacement

plotted against normalized modulus of subgrade reaction is presented in Figure 3.8,

which shows that the normalized pile head displacement is independent of EI. The

relationship between normalized pile head displacement and normalized modulus of

subgrade reaction (K/Kref) can be written as:

75.0−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

refref KK

uu

(3.2)

71

By equating the normalized pile head displacement from Eq. (3.1) based on the 3-

D finite element analyses and Eq. (3.2) based on the subgrade reaction theory, the

relationship between pile diameter and modulus of subgrade reaction can be obtained as:

364.0

⎟⎟⎠

⎞⎜⎜⎝

⎛=

refref DD

KK

(3.3)

The relationship based on the above expression is graphically illustrated in Figure

3.9 together with two different concepts regarding pile diameter effect on modulus of

subgrade reaction. It is observed that Terzaghi’s concept (1955), in which the modulus of

subgrade reaction is independent of pile diameter, is conservative. However, the

modulus of subgrade reaction derived from Carter’s concept (1984) is too large for the

linear elastic case.

Eq. (3.3) implies that in order to double the modulus of subgrade reaction, the pile

diameter needs to be increased by about 7 times. If the pile diameter is doubled, the

modulus of subgrade reaction will increase by only 30%. In reality, increasing the pile

diameter also increases the stiffness of the pile (EI). If the pile is a solid circular section,

increasing the pile diameter by 2 times increases the pile stiffness by 16 times. Figure

3.10 presents a comparison of pile response (i.e., pile head displacement and ratio of

maximum moment to yield moment) due to the change of pile diameter. It can be seen

that the pile diameter has more effect on the pile head displacement than the maximum

moment. Increasing pile diameter by 10 times decreases the pile head displacement by

50%, while the maximum moment was decreased by only 20%. It is noted that the yield

moment, My, of the reference pile was assumed to be the same as the maximum moment

occurred in that pile, and thus the yield stress of this material, σy, could be computed

using the basic strength of materials (i.e., yyDM σπ32

3

= ). The yield moment for other

pile diameters was then calculated in the same fashion. The improvement of lateral pile

72

response due to the effect of increasing soil modulus of subgrade reaction with the pile

diameter is significantly less than that due to the change in pile stiffness (EI) with pile

diameter, particularly for the ratio of the maximum moment to the yield moment.

Furthermore, the improvement of the pile response due to the combined effect of both

soil and pile is insignificant compared with the case when considered only the effect from

the increase of pile stiffness. In other words, for the linear elastic case, increasing pile

diameter increases the lateral soil resistance (i.e., the modulus of subgrade reaction),

resulting in the improvement of lateral pile response. However, this effect is

overshadowed by a significant improvement of pile stiffness as the pile diameter

increases.

According to the results of the linear elastic case, pile diameter has a small effect

on pile response when considering only the effect from the soil. It is interesting to pursue

the study of pile diameter effect using the same mesh, but changing the soil properties

from linear to the elasto-plastic soil model. This will allow us to understand the trend of

pile diameter effect on the response of laterally loaded piles due to the effect of soil

nonlinearity.

3.3 Elasto-Plastic Soil Model

The meshes from the previous analyses were reused in this section by modifying

the soil properties from a linear material to an elasto-plastic material with hardening,

using 3-D J2 plasticity model with von-Mises yield criterion and a linear hardening law

(Taylor 1998). This model was used because it was the only 3-D nonlinear model

available in FEAP. The same modulus and Poisson’s ratio of the soil from previous

study were incorporated with nonlinear parameters used for specifying the yielding and

hardening portion of the soil. The yield shear stress for the soil in this case was 34.5

kN/m2 and the kinematic hardening modulus was 275.8 kN/m2. Though the soil

properties used in the analyses were not directly related to the typical soil parameters

73

used in geotechnical engineering (i.e., friction angle and cohesion), the analyses is useful

for indicating how the pile diameter effect changes due to the nonlinearity of the soil.

Extensive studies were conducted to determine the optimal number of time steps and

iterations to ensure that the solution converged before conducting the study. It was found

that with 40 time steps and 10 iterations, the solution had sufficient accuracy, and that

was used throughout the analyses.

Figure 3.11 presents the comparison of moment profiles for both linear and

nonlinear cases for different pile diameters with a horizontal pile head load of 890 kN. It

is seen that the maximum moment became larger and its location became deeper when

the nonlinear soil properties were used. The maximum moment and its location for the

nonlinear case follows the same trend as the linear case in which the maximum moment

increased and its location moved toward the ground surface as the pile diameter increased.

Figure 3.12 presents the normalized pile head displacement (u/uref) against normalized

pile diameter (D/Dref) for nonlinear and linear cases at different horizontal loads. It

indicates that the effect of pile diameter becomes more significant when the soil behavior

changes from linear to nonlinear. The pile diameter effect depends on the loading level.

Increasing the pile head horizontal load yields greater nonlinearity and thus increases the

pile diameter effect on pile response. In addition, it can be expected that the pile

diameter effect depends upon the degree of nonlinearity of the soil. The higher degree of

soil nonlinearity, the greater the pile diameter effect on the soil-pile response.

As the soil in its nature is nonlinear, it is worthwhile to evaluate the influence of

pile diameter on the response of lateral load pile in real soil. To accomplish this, a series

of full-scale lateral load tests on CIDH piles were carried out and are discussed in the

following chapters. The details of test setup and test results will be given in the next

chapters.

74

3.4 Limitation of 3-D Finite Element Model

Due to the simplicity of the 3-D finite element model used in this study, some

other important aspects could not be incorporated, which may have significant

contributions to the effect of pile diameter on the pile response. These include soil-pile

separation, friction between the soil and pile, and the effect of soil confinement. Further

research in this area with a better 3-D model, that allows incorporation of these important

aspects, is important to provide better understanding on the effect of pile diameter on the

pile response. The results of full-scale lateral pile load tests are, however, needed as a

baseline to calibrate the finite element model. Once the model has been verified with the

experimental test results, the investigation of other aspects can then be studied.

3.5 Summary

The 3-D finite element method was used to model the soil-pile structure

interaction problem to evaluate the effect of pile diameter on pile responses. Both linear

and nonlinear soil model was considered in the analyses. Though the pile diameters were

varied, the pile stiffnesses were kept to be constant throughout the analyses. Results from

the analyses shows that pile diameter has some effect on the pile response (i.e. pile head

displacement and moment distribution). Increasing the pile diameter appears to decrease

the pile head displacement, the maximum moment, as well as lower the depth to

maximum moment. However, pile diameter effect on the pile response seems to be very

small when considering the effect of increasing pile stiffness with the pile diameter. In

addition, the nonlinearity of the soil increases the effect of pile diameter on the pile

response.

Though results from the analyses provide insight into pile diameter effect on the

pile response to some extent, the simple model used in the analyses could not cover all

aspects which are actually present in the actual behavior of the soil-pile interaction.

75

Therefore, the full-scale testing on different diameters of CIDH piles was carried out to

investigate pile diameter effect experimentally as presented in the following chapters.

76

Figure 3.1 Finite Element Mesh for Pile Diameter Effect Study

Plan

Rigid Link

x

y

z

Pile (Beam Element)

Section

77

1

1

1

1

1

S T R E S S 1

1 -2.000E+00

2 -7.000E+00

3 -1.200E+01

4 -1.700E+01

5 -2.200E+01

6 -2.700E+01

7 -3.200E+01

8 -3.700E+01

Time = 0.00E+00Time = 0.00E+00

1

11 1

1

11

1

2

1

2

1

1

DISPLACEMENT 1

1 1.176E-01

2 2.682E-01

3 4.188E-01

4 5.694E-01

5 7.200E-01

6 8.706E-01

7 1.021E+00

8 1.172E+00

Time = 0.00E+00Time = 0.00E+00

Figure 3.2 Typical Results of Compression Stress (σx) and Displacement in Soil in Laterally Loaded Pile Problem

Stress (σx) (kPa) 1. -13.8

2. -48.3

3. -82.7

4. -117.2

5. -151.7

6. -186.2

7. -220.7

8. -255.2

Horizontal Displacement (mm) 1. -3.0

2. -6.8

3. -10.6

4. -14.5

5. -18.3

6. -22.1

7. -25.9

8. -29.8

a)

b)

78

0 0.2 0.4 0.6 0.8 1 1.2Pile Diameter, D (m)

0

20

40

60

80

100

Pile

Hea

d D

ispl

acem

ent,

u (m

m) FEM

Elastic Continuum (Davies and Budhu 1986)

Figure 3.3 Comparison of Pile Head Displacement obtained from 3D FEM and Elastic Solution

79

020

040

060

080

0

Mom

ent (

kN-m

)

1612840

Depth (m)

0.15

m0.

46 m

0.76

m1.

07 m

Dia

met

er

010

2030

4050

Dis

plac

emen

t (m

m)

1612840

Depth (m)

0.15

m0.

46 m

0.76

m1.

07 m

Dia

met

er

(a)

(b)

Fi

gure

3.4

Ef

fect

of P

ile D

iam

eter

on

Pile

Res

pons

es (a

) Mom

ent ,

and

(b) D

ispl

acem

ent

80

0 2 4 6 8Normalized Pile Diameter, D/Dref

0

0.2

0.4

0.6

0.8

1

1.2

Nor

mal

ized

Pile

Hea

d D

ispl

acem

ent,

u/u r

ef

FEMCurve Fitting

u/uref = (D/Dref)-0.273

Figure 3.5 Normalized Pile Head Displacement against Normalized Pile Diameter

81

-200

020

040

060

080

0

Mom

ent (

kN-m

)

1612840

Depth (m)

3D F

EM

LPIL

E

-20

020

4060

Dis

plac

emen

t (m

m)

1612840

Depth (m)

(a)

(b)

Fi

gure

3.6

C

ompa

rison

of P

ile R

espo

nses

obt

aine

d fo

rm 3

D F

EM a

nd L

PILE

(a) M

omen

t , a

nd (b

) Dis

plac

emen

t

82

0 20000 40000 60000 80000Modulus of Subgrade Reaction, K (kN/m2)

0

10

20

30

40

50

60

70

80

Dis

plac

emen

t, u

(mm

)EI0.5EI

Decrease EI

Figure 3.7 Displacement at Pile Head against Modulus of Subgrade Reaction

0 1 2 3 4 5 6Normalized Modulus of Subgrade Reaction, K/Kref

0

0.2

0.4

0.6

0.8

1

1.2

Nor

mal

ized

Pile

Hea

d D

ispl

acem

ent,

u/u r

ef

u/uref = (K/Kref)-0.75

2 Data Sets

Figure 3.8 Normalized Pile Head Displacement against Normalized Modulus of Subgrade Reaction

83

1 2 3 4 5 6 7 8 9 10Normalized Pile Diameter, D/Dref

0

1

2

3

4

5

6

7

8

9

10

Nor

mal

ized

Mod

ulus

of S

ubgr

ade

Rea

ctio

n, K

/Kre

f

TerzaghiCarter3D-FEM

Figure 3.9 Comparison of Two Different Concepts on Pile Diameter Effect on Modulus of Subgrade Reaction with Results from 3-D FEM

84

0 2 4 6 8 10 12Normalized Pile Diameter, D/Dref

0

0.2

0.4

0.6

0.8

1

1.2

Nor

mal

ized

Pile

Hea

d D

ispl

acem

ent,

u/u r

ef

SoilPileSoil+Pile

0 2 4 6 8 10 12Normalized Pile Diameter, D/Dref

0

0.2

0.4

0.6

0.8

1

1.2

Rat

io o

f Max

imum

Mom

ent

to Y

ield

ed M

omen

t, M

max

/My

SoilPileSoil+Pile

(a)

(b)

Figure 3.10 Effect of Pile Diameter on Lateral Pile Responses (a) Pile Head Displacement, and (b) Ratio of Maximum Moment to Yield Moment

85

-400 0 400 800 1200 1600

Moment (kN-m)

20

16

12

8

4

0

Dep

th (m

)

LinearNonlinear

0.15 m0.46 m0.76 m

Diameter

Figure 3.11 Comparison of Moment Profiles for Linear and Nonlinear Analyses

86

0 2 4 6 8Normalized Pile Diameter, D/Dref

0

0.2

0.4

0.6

0.8

1

1.2

Nor

mal

ized

Pile

Hea

d D

ispl

acem

ent,

u/u r

ef

LinearNonlinear

Figure 3.12 Comparison of Normalized Pile Head Displacement against Normalized Pile Diameter for Linear and Nonlinear Analyses

87

Chapter 4 FULL-SCALE TESTING

The results of the 3-D finite element analyses in the previous chapter showed that

the effect of pile diameter on pile response increases as the soil behavior changes from

linear to nonlinear. The motivation from the analytical results leads to further

investigation on the pile diameter effect in real soil where the nonlinearity is expected by

its nature. Full-scale testing programs including vibration and lateral load testing were

carried out to fulfill the aim of this study. The results from the vibration tests were used

to study the behavior of soil-pile interaction at small strain, as well as to evaluate the pile

diameter effect when the soil is linearly elastic. The results from the full-scale lateral

load test were used to assess the pile diameter effect at larger strain levels where the soil

behavior becomes nonlinear, as well as to evaluate the seismic performance of CIDH

piles.

In this chapter, the site characterization is first discussed to give an overview of

the site conditions and the strength characteristic of the soil at the test site. This is

followed by the pile description which includes the pile geometry, reinforcement details,

and pile instrumentation. Finally, the testing procedure and testing programs for both

vibration and lateral load tests on CIDH piles are described.

4.1 Site Description

The test site is located immediately east of Interstate 5 at the University of

California, San Diego, known as UCSD East Campus. It is located southwest of Parking

Lot 702 and southeast of a baseball field. The location map of the UCSD East Campus

test site is shown in Figure 4.1. The test site is relatively flat, and is bounded on north

and west by moderate to steep canyon slopes. The test specimens were located within the

test site to avoid any slope effects. The topographic map of this site is presented in

Figure 4.2.

88

According to available geologic literature (GEOCON, 1986 and Elliot, 1988), the

soil formation of UCSD East campus property is underlain by the Eocene-aged Scripps

Formation, the Pleistocene-aged Linda Vista Formation and four types of surficial

deposits consisting of alluvium, colluvium, topsoil and landslide deposits. The Scripps

Formation, a marine sedimentary deposit, generally consists of light brown and gray,

weakly cemented silty sand interbedded with sandy siltstone, with clay beds and seams.

Very hard cemented concretions occur frequently within this formation. The Linda Vista

Formation, a non-marine and marginal marine sedimentary deposit, overlies the Scripps

Formation. It consists of very dense, reddish-brown, cemented, clayey sand and

occasional cobble conglomerates. The colluvial/ alluvial deposits are typically composed

of loose, porous, silty clay/ clayey sand that have accumulated near the base of slopes or

along canyon bottoms. The topsoil consists of loose, silty, dark grayish-brown, fine

sands as well as clayey sands. Quaternary landslide deposits typically consisting of slide

scarps and hummocky slide mass topography are commonly observed in the field, on

topographic maps and stereographic aerial photographs. Though all these soils are found

on East Campus, only the Scripps Formation is present at the test site as indicated in the

geologic map in Figure 4.3.

Apart from the available literatures, a subsurface exploration was conducted to

obtain more geotechnical information of the test site. The exploration work was started

on September 2, 1998 and was completed on September 3, 1998. Two boreholes were

drilled to depths of 20 m and 24 m by means of a percussion drilling method. The

ground water table was not encountered during the soil investigation. The locations of

both boreholes are presented in Figure 4.4. The Standard Penetration Test (SPT) was

carried out to determine the strength characteristics of the soil. Soil samples were also

collected at several depths by using split-spoon samplers for soil classification.

Gradation analysis tests (ASTM 1998) using the wet-sieve method (ASTM D1140-97)

were performed on the soil samples to determine the soil types as given in Appendix-A.

Soil at this site consists of light brown and gray to dark brown, medium dense to very

89

dense cemented clayey to silty sand. According to the unified soil classification system:

ASTM D2487-93 (ASTM 1998), the soil was classified as SC and SM. The corrected

SPT N-values, (N1)60 –values, varied from 16 to approximately 50 for the first 6 m.

Below this layer, the (N1)60 –values exceed 50. The SPT N-values were corrected based

upon a hammer type and release system, sampler configuration, short rod lengths, and

overburden stresses. Lenses and seams of siltstone and sandstone were found at various

depths. Clay and silt (CL and ML) beds were also encountered. The soil boring log of

each borehole is shown in Figure 4.5 and Figure 4.6. The corrected SPT N-value profile

is presented in Figure 4.7a. In addition, the shear wave velocity profile was measured

using the seismic down-hole technique. The travel-time curve together with calculated

shear wave velocity is presented in Figure 4.7b. This type of stepped profile is common

in weakly cemented sands (e.g. Ashford and Sitar 1994).

By the nature of weakly cemented sand, undisturbed soil samples are extremely

difficult to obtain. The typical procedure used in California to characterize the shear

strength of this particular type of soil is penetration resistance using the Modified

California sampler. Direct shear tests on the driven samples are also occasionally

conducted to evaluate the shear strength, but represent somewhat the lower bound values

due to significant degree of soil disturbance during the sampling. In order to further

understand the characteristics of the weakly cemented sand from the Scripps formation,

additional soil data was extracted from available soil reports conducted at UCSD by local

geotechnical engineering firms. The locations of soil investigation sites are presented in

Figure 4.8, each site having three to eleven borings. Sites B-1 and B-2 were located in

the direct vicinity of the test site. The blow count values using California sampler of the

Scripps formation are more than 50, representing very dense sand. A summary of the

blow counts of each borehole is given in Appendix B. Direct shear tests on driven soil

samples were also conducted with cohesion ranging from approximately 15 kN/m2 to 55

kN/m2 and the angle of friction varying between 30 degrees and 32 degrees. The dry

density of this formation ranged from 14.6 kN/m3 to 19.2 kN/m3 with an average value of

90

17.1 kN/m3. The moisture content varied between 5.4 % and 20.6% with an average

value of 10.4%. A summary of soil properties are provided in Appendix B. The same

soil formation also exists in several other locations on the UCSD campus. The soil

properties of this formation at some locations further away from the test sites (i.e., site C-

1, C-2, and C-3 in Figure 4.8) are summarized in Appendix C. Similar soil

characteristics were observed with blow count values of more than 50. The results from

direct shear tests show that soil cohesion ranged from approximately 36 kN/m2 to 53

kN/m2, and the friction angle varied between 20 degrees and 34 degrees. The dry density

varied between 13.0 kN/m3 and 19.2 kN/m3 with an average value of 16.4 kN/m3. The

average moisture content is 15.8%.

In summary, the Scripps formation has the SPT N-values of more than 50, as a

results the friction angle of 45 degree is suggested. The average dry unit weight of 17

kN/m3 appears to be reasonable for this type of soil deposit with the water content of

about 12%. Comparing the strength characteristic of this formation obtained from the

subsurface investigation at the test site and data obtained from the local geotechnical

firms, the soil condition at the test site appears to represent the lower bound soil strength

of this formation.

4.2 Description of Test Piles 4.2.1 Pile Geometry and Section Reinforcement Details

Four different diameters of CIDH piles were designed and installed at the UCSD

test site ranging in diameter from 0.4 m to 1.2 m. The 0.4-m CIDH pile was 4.5 m long

and all others were 12 m long, though all acted as “long piles” (i.e., the piles were long

enough that the lateral response was independent of depth.). A longitudinal

reinforcement of 2% (i.e. volumetric ratio of longitudinal steel) and a transverse

reinforcement of 0.6% (i.e. volumetric ratio of transverse steel) were used. The concrete

cover of each pile was approximately 50 mm. The section reinforcement details of each

91

pile are presented in Figure 4.9. The reinforcing steel of the 0.4-m CIDH pile comprised

13- 15.9 mm (#5) bars with 9.5 mm (#3) spiral spaced at 152 mm intervals. The 0.6-m

CIDH pile consisted of 15-22.2 mm (#7) with 9.5 mm (#3) spiral spaced at 89 mm

intervals. The reinforcing steel of the 0.9-m CIDH pile consisted of 26- 25.4 mm (#8)

bars with 12.7 mm (#4) spiral spaced at 102 mm intervals. The reinforcing steel of the

1.2-m CIDH piles contained 28- 32.3 mm (#10) bars with 15.9 mm (#5) spiral spaced at

121 mm intervals. A total of three specimens of each bar diameter were tested. The

stress-strain curves from the tensile tests for each bar size are summarized in Figure 4.10

and Figure 4.11. The amount of transverse reinforcement was chosen to be lower than

that specified in Caltrans Bridge Design Specifications, BDS (Caltrans 2000) because the

effect of soil confinement in enhancing the inelastic behavior of CIDH piles was

expected. According to Article 8.18.2.2.2 in BDS, the minimum ratio of spiral

reinforcement in potential plastic hinge zone ρs shall not be less than:

for column 0.9 m or less

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

gc

e

y

c

c

gs Af

Pff

AA

'25.15.0

'145.0ρ (4.1)

or

for column larger than 0.9 m

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

gc

e

y

cs Af

Pff

'25.15.0

'12.0ρ (4.2)

But not less than the value given by

y

c

c

gs f

fAA '

145.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛−=ρ (4.3)

92

where fc’ = concrete compression strength, fy = yield strength of the spiral but cannot

exceed 414 MPa, Pe = axial load, Ag = area of gross section, and Ac = area of core section.

According to this specification and the material properties of the pile, the

minimum transverse reinforcement for each pile was calculated as summarized in Table

4.1. It should be noted that the amount of transverse reinforcement ratios compared to

those recommended by BDS varied from 22% for the 0.4-m pile to 85% for the 1.2-m

pile.

The piles were built and installed in two different periods. The 0.6-m and 0.9-m

piles were installed in September 1998 (Phase I). The remaining piles were installed in

September 2000 (Phase II). The piles were installed by using the Cast-In-Drilled–Hole

(CIDH) method. The ground was drilled with a required diameter to a specified depth.

After that, the instrumented steel cage was lowered into the drilled hole. The drilled hole

was then filled with concrete. Figure 4.12 present sequence of an installation of a CIDH

pile. The pile shaft above the ground and load stubs were constructed and cast

approximately one month after the pile installation. Figure 4.13and Figure 4.14 present

the preparation and construction of load stubs. The target compressive strength at 28

days of each pile was f’c= 24.1 MPa. However, the actual compressive strengths were

higher. The average compressive strength of concrete for each pile is given in Table 4.2.

4.2.2 Instrumentation of Test Piles

In this section, the instrumentation of test piles for lateral load testing is

described, while that for vibration testing will be given in the following section. Several

types of instrumentation (i.e., strain gauges, tiltmeters, load cells, and linear

potentiometers) were installed on each pile specimen to measure pile responses under

lateral loading. Strain gauges were instrumented along four longitudinal bars of each

pile to obtain the bending moment along the pile. For the 0.6-m and 0.9-m piles, two

instrumented longitudinal bars were approximately aligned with the loading direction and

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the other two were perpendicular to the loading direction. However, the locations of

instrumented strain gauge bars were modified for piles constructed in Phase II (i.e., 0.4-m

and 1.2-m piles) to provide more information in estimating the pile curvature. Two

instrumented longitudinal bars were aligned approximately with the loading direction.

The other two were evenly spaced between them. The locations of strain gauge bars for

each pile are presented in Figure 4.9. Strain gauges were attached along the pile length

with closer spacing for the upper portion and wider spacing for the lower portion. The

locations of strain gauges for each pile are summarized in Table 4.3. Furthermore, strain

gauges were also attached along the spiral of the 0.6-m and 0.9-m CIDH piles for the first

3m below the ground surface to measure shear strain in the piles. The directions of these

strain gauges were similar to bending strain gauge direction.

A series of tiltmeters were installed along the pile to monitor pile rotation during

lateral load testing. They were used for computing the pile deflection as well as backing

up the strain gauge data. For the 0.6-m and 0.9-m piles (Phase I), the tiltmeters were

installed by tightening them with the reinforcing steel at depths of 0 m, 0.9m, 1.8m and

2.7 m. As a result, they could not be reused after the test. Considering the cost and the

amount of tiltmeters required for each test, a system was specially designed and

fabricated such that tiltmeters could be inserted into the inclinometer tube. With this

design the tiltmeter can be pulled out after the lateral load test and reused for the next

tests. Figure 4.15 shows a method in installing tiltmeters in the inclinometer casing. This

type of system was used for the 0.4-m and 1.2-m piles in Phase II. A summary of

locations of tiltmeters for each pile is given in Table 4.3. The other instrumentation,

including linear potentiometers and load cells for providing the load-displacement curves,

is discussed in the test setup for lateral load testing section because their locations depend

on the configuration of each test setup.

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4.3 Vibration Testing

Prior to the lateral load testing, extensive vibration tests were conducted to

determine the dynamic properties of the soil-pile system (i.e., natural frequency, damping,

and mode shape) and to evaluate the pile diameter effect at a small strain level where the

soil and the pile can be considered as a linear elastic material. Various types of vibration

tests including ambient, impact, and forced vibration tests were carried out prior to

conducting the lateral load test. These vibration tests were intended to determine the

dynamic properties of the soil-pile system at small strain. In this section, the descriptions

of instrumentation and data acquisition system are provided. This is followed by the

descriptions of the testing procedure as well as the testing program.

4.3.1 Description of Instrumentation

4.3.1.1 Accelerometers

Two different types of accelerometers were used for the vibration testing. The

PCB Model 393 C accelerometer is a very sensitive and robust accelerometer and it is

suitable for most types of vibration testing, especially for very small vibration tests. The

PCB accelerometer has a frequency range between 0.025 and 800 Hz, an amplitude range

of +2.5g, and a resolution of 0.0001g. They were attached on the load stub in N-S and E-

W direction to measure the pile response during vibration.

The crossbow Model LF series accelerometer has an amplitude range of +2g with

a resolution of 0.0012g. The crossbow accelerometers LF series were only used for the

forced vibration test at resonant frequency because they are small and therefore could be

inserted into the pile via inclinometer tubes to measure the response of the pile at its

resonant frequency, thus allowing it to obtain the mode shape. A series of the crossbow

accelerometers were inserted into the inclinometer tube by means of attaching them to the

inclinometer accessories. The locations of the accelerometers for the forced vibration

95

tests at a resonant frequency of the 0.4-m and 1.2-m CIDH piles are presented in Figure

4.16.

4.3.1.2 Modal Hammer PCB 086 C50

The modal hammer PCB 086 C50 (Figure 4.17) was used to excite the pile to

measure the dynamic properties of soil-pile system in the impact test. The hammer

weighs 5.4 kg and has a head diameter of 75 mm. The hammer includes a series of four

removable rubber tips for modifying the amplitude of the applied force and the frequency

range of excitation.

4.3.1.3 Mass Shaker

An eccentric mass shaker was used for the forced vibration test to generate

sinusoidal dynamic force to the piles. The mass shaker (Figure 4.18) used in this study

was initially designed and constructed at RPI (Van Laak and Elgamal 1991) based on the

original Hudson (1964) design. Originally, the shaker was designed to provide up to 22

kN of horizontal shaking force within a frequency range of 0.5-30 Hz. To achieve this

wide range of operating frequencies without exceeding the shaker-load capacity, both

mass and eccentricity of the counter rotating elements are designed to be conveniently

changed during testing by adding lead plates in the counter rotating steel buckets up to 10

Hz (Hudson 1964), or by replacing these buckets with eccentric steel masses (15.1 kg

each) in the operational range of 10-30 Hz (Van Laak and Elgamal 1991). Though the

shaker has the capability to handle a wide range of frequency interest, the amplitude of

the dynamic force produced by the shaker with available types of buckets appeared to be

too large for the test piles and could have caused significant disturbance to the soil-pile

system before lateral load testing. The eccentric aluminum buckets (Figure 4.19) based

on the original design of steel buckets were therefore designed and constructed to

decrease the level of dynamic force produced by the shaker. The aluminum buckets

were designed in such a way that the amplitude of dynamic force can be varied up to 4

96

different levels by adding the aluminum plates to the buckets (i.e., empty bucket (0.65

kg), one aluminum plate (1.46 kg), two aluminum plates (2.06 kg), and a full bucket

(2.65 kg)). The relationship between amplitude of dynamic force and frequency

excitation at different bucket masses is presented in Figure 4.20. A DC motor and

electronic controller was used to drive the eccentric masses. The rotational speed of the

shaker was verified to remain stable at any specified frequency within a 0.0625 Hz range.

4.3.1.4 Recording and Data Processing Instruments

The HP 3566A dynamic analyzer was used to collect and process the data during

testing. With this system, processing dynamic data in both time and frequency domains

can be performed (e.g., power spectrum, frequency response, time/linear spectrum, and

etc.). The description of the analyzer and signal conditioner is briefly provided.

HP Analyzer

The HP 3566A is an expandable analyzer that characterizes signals in both time

and frequency domains. The analyzer uses an MS-DOS operating software and

Microsoft Windows based user interface. The HP 3566A has 16 channels and a

maximum frequency bandwidth of 12.8 kHz on each channel. Its specialty is multi-

channel measurements and monitoring at low frequencies. The HP 3566A measurement

hardware consists of a HP 35650A mainframe containing the following modules:

• 1 HP 35651C HP-IB/signal processor module

• 2 HP 35655A 8-channel input modules

• 1 HP 35653C source module

Signal Conditioner

The model 583 multi-channel signal conditioner is designed for powering

piezoelectric sensors and provides an effective method for managing large numbers of

sensor channels. The model used in this study has 16 channels.

97

4.3.2 Testing Procedure

4.3.2.1 Ambient Vibration Test

The naturally occurring vibration of the test piles embedded in the soil caused by

wind and other environmental factors were measured during the ambient vibration test to

yield the natural frequencies of the soil-pile systems. A power spectrum measurement

was chosen to obtain the values of frequency components because the signal analyzer

allowed for averaging the results of many runs, thus smoothing out the signal. In this

case, a total of 100 runs were used for each test. The ambient vibration tests were

performed on all piles. However, for the 1.2-m diameter pile where the magnitude of

vibration was approximately noise level and the peak representing the natural frequency

of the system could not be observed therefore the results of the ambient vibration test for

the 1.2-m piles will not be presented. In some tests, an additional mass (220 kg) from the

mass shaker was added to the system by mounting it on the load stub so as to decrease the

natural frequency of the system.

4.3.2.2 Impact Vibration Test

Frequency response measurement was used for the impact vibration test, which

shows the ratio of the measured output to the input stimulus. The load stub was hit by a

modal hammer with a load cell and a rubber tip to generate an initial velocity to the pile

(Figure 4.21). The response under a free vibration of the pile was recorded using

accelerometers. In this case, the input stimulus is the force that was applied to the load

stub and the output is the acceleration of the load stub. A total of 10 hits per test were

conducted for averaging the signal. The locations of accelerometers for this test were

similar to those of ambient vibration test.

98

4.3.2.3 Forced Vibration Test

For the forced vibration test, a mass shaker (harmonic oscillator) was mounted on

the top of the pile to generate the sinusoidal excitation force (Figure 4.22). A series of

frequency sweeps using sinusoidal excitation were performed. The pile was excited at a

specific frequency until the steady-state response was attained and the pile response was

recorded. The frequency of excitation was then increased and the process was repeated

to obtain the response curve of which the resonant frequency of the system can be

determined from its peak. For each set of resonant frequency test, the harmonic forced

vibration tests were repeated at least 3 times to ensure that the constant of resonant

frequency was obtained. The pile was then shaken at the resonant frequency and data

from several crossbow accelerometers as well as strain gauges along the piles were

recorded. With this data, the mode shape of the system can be computed. The effect of

the level of dynamic force to the natural frequency of the system was also studied by

adding more aluminum plates to the buckets resulting in an increase in the amplitude of

excitation.

4.3.3 Testing Program

In general, the testing program for vibration tests for each pile was essentially the

same. The ambient and impact vibration tests were first performed before the forced

vibration test to obtain the natural frequency of soil-pile system under undisturbed soil

condition. Subsequently, the forced vibration test was conducted to obtain the dynamic

properties at a higher strain level. A summary of testing program for vibration testing for

each pile is given in Table 4.4 through Table 4.8.

4.4 Lateral Load Testing

After the completion of vibration tests, a series of lateral load tests were

performed under both static and cyclic loading to study pile diameter effect on p-y curves

99

as well as evaluate inelastic behavior of CIDH piles with the effect of soil confinement.

In this section, the test setup, testing program and testing procedure of each test are

described.

4.4.1 Test Setup

A total of 4 lateral load tests were carried out. The first lateral load test was

conducted in December 1999 (Phase I). The others were conducted in November 2000

(Phase II). The testing sequence is illustrated in Figure 4.23. One or two 2200-kN

hydraulic actuators were connected between two piles to provide the lateral load to the

test specimens. The larger pile served as a reaction pile to test the smaller one. The load

acting on the specimen was measured by load cells in the actuator. Several string-

activated linear potentiometers were attached to each pile to monitor pile displacements

as well as load-displacement curves. The locations of string-activated linear

potentiometers for each test are presented in Figure 4.24 through Figure 4.27 together

with the locations of the other instruments (i.e., strain gauges and tiltmeters), which were

connected to a data acquisition system. Figure 4.28 presented a photograph of lateral

load test setup for the 0.6-m CIDH pile against the 0.9-m CIDH pile.

4.4.2 Data Acquisition System

Data from various instruments was collected through a high-speed data

acquisition system with the LabVIEW computer software (National Instrument1998) to

acquire and manipulate the data during the test. The system was housed inside the UCSD

mobile field testing laboratory as presented in Figure 4.29. The system consisted of a

SCXI signal conditioner manufactured by National Instruments, and a DaqBoard to

covert the conditioned analog signal into a corresponding digit number with a maximum

scan rate of 100 kHz. The SCXI conditioner consisted of 4 SCXI 1001 chassis, 4 SCXI

1120 modules, 44 SCXI 1121 modules, 4 SCXI 1320 terminal blocks, and 44 SCXI 1321

terminal blocks having a capability to handle up to a total of 200 channels. The SCXI

100

1001 is a rugged, compact 12-slot chassis that is able to house the SCXI modules. The

SCXI-1120 module is the 8 channel isolation amplifiers used for acquiring and changing

the raw transducer signal (i.e., tiltmeter, load cell, and linear potentiometers) into a

standardized voltage output. The SCXI-1121, which can also offer excitation sources for

each channel, was used to acquire and manipulate the signal from strain gauges. The

SCXI-1320 and 1321 terminal blocks provide a convenient method for connecting and

disconnecting the signal to the SCXI modules.

4.4.3 Testing Program and Testing Procedure

The lateral load testing procedure for each pile was essentially the same. The

sequence of a lateral load test can be divided into 3 categories: static load test, cyclic

load test before idealized yield, and cyclic load test after idealized yield. The standard

testing procedures are given as the following:

First, the static load test was performed to obtain the load-displacement

information under static loading so as to develop p-y curves for each pile. The loading

procedure was conducted in general accordance with ASTM standard (ASTM 1998) with

standard loading procedure: ASTM D3966-90. The test pile was pushed against the

reaction pile until the load reached a target level. Then, the load was maintained for

either 10 minutes or 20 minutes depending on the load level to allow the pile

displacement to stabilize before the next step of loading. Afterward, the next load

increment was applied and the same procedure was repeated. The specimen was loaded

to 12.5%, 25%, 37.5%, 50%, 62.5%, 75% and 85% of the idealized yield load. After that,

the pile was unloaded to 75%, 50% and 25% of yield load, and at each unloading step,

the load was maintained for 10 minutes. The pile was then unloaded to zero. After a

completion of the lateral static load test, the test pile was pulled back to its original

position and then the cyclic load test was started. It should be noted that due to the error

of estimation of the yield load based on the available p-y curves, the actual loading

scheme for each test was slightly different from the planning stage.

101

Second, the cyclic load test before the idealized yield of the pile was performed to

study the strength degradation of pile-soil system due to an increase of number of load

cycles. The pile was cycled 25 times at each step of loading for the 0.6-m pile. For the

other piles, the number of cycles was decreased to 10 times because test results from the

0.6-m pile indicated that after the 5th cycle, no strength degradation was observed. The

pile was loaded to the displacements at +12.5%, +25%, +37.5%, +50%, +62.5%, +75%,

+87.5% and +100% of the idealized yield load. The displacement at the idealized yield

load was estimated based on the test results from the static test. A ramp rate between

0.64 mm/s and 2.5 mm/s was applied during the test.

Finally, the cyclic load test was conducted after the idealized yield of the pile in

order to study seismic pile performance. The pile was cycled 3 times to approximately

+150%, +200%, +250%, +300%, +400%, +500% and +600% of displacement at

idealized yield corresponding to a displacement ductility of 1.5, 2.0, 2.5, 3.0, 4.0, 5.0 and

6.0, respectively. Since the actuator capacity in the pull direction was limited to only 980

kN, some displacement targets in the pull direction could not be achieved. Furthermore,

it should be noted that there were some problems in controlling the actuator during lateral

load test no.4, making the actual procedure slightly different from the planning stage.

Details of test procedure of individual tests are given as the following:

4.4.3.1 Lateral Load Test 1

The detail of the static test of the 0.6-m pile was different from the standard

procedure given above. Unlike the other tests in which the piles were tested under load

control, the test on the 0.6-m pile was conducted under displacement control. The load-

displacement relationship for the 0.6-m diameter CIDH pile was first analyzed using the

FLPIER computer program (University of Florida 1996) to develop the loading scheme

that was implemented in the testing procedure. Based on the prediction, the displacement

at the ground surface at idealized yield of the pile was approximately 3.2 mm with the

ultimate load capacity around 250 kN. However, due to the uncertainty of soil and

102

material properties, as well as the doubt in accuracy in implementing the existing sand p-

y curves (Reese et al. 1974) for weakly cemented sand, the displacement of 25.4 mm was

chosen to be the displacement at idealized yield. It was implemented in this way to

decrease the risk in yielding the pile during the static test. The lateral load testing was

conducted by pulling towards each other until it reached a specified displacement. The

specimen was loaded to approximately +12.5%, +25%, +50%, +75% and +100% of the

computed idealized yield displacement. At each step of loading, the load was maintained

for 10 minutes to allow the displacements of the piles to be stabilized. The load was

maintained for 20 minutes at the last loading step. Subsequently, the load was decreased

to +50%, +25% and 0% of the computed idealized yield displacement.

To study the strength degradation of the pile-soil system due to an increase of

number of load cycles, the pile was cycled 25 times at each step of loading. The pile was

loaded to +6.25%, +12.5%, +25%, +50%, +75% and +100% of the computed

displacement at idealized yield.

The 0.6-m diameter pile was then cycled 3 times to +150%, +200%, +300%,

+400%, +600% of displacement at computed idealized yield to evaluate the seismic

performance of the pile. An increase in the displacement of the pile was continued until

the 0.6-m diameter pile reached failure.


The procedure of static load test was the same as the standard procedure given

above. However, the actual yield load was lower than the predicted one (i.e., 1690 kN)

causing the pile to yield at 75 % of the predicted yield load (i.e. 1112 kN). It was found

that the actuator load measured in the first test should be reduced by 25% likely due to

the human error. More details are discussed in the next chapter. Since the pile was

yielded before the target load, the static loading procedure was adjusted by unloading

from 75% to 50%, 25% and 0% of predicted yield load with maintaining the load for 10

103

minutes at each step. After that, the pile was pulled back to the original position and the

cyclic load test was started by following the standard cyclic loading procedure as

mentioned above. The pile was tested until the displacement of the pile head reached the

capacity of a linear potentiometer.


The prediction of the load-displacement curve was made before the test in order

to estimate the yield load and the yield displacement using the results from the previous

test. The predicted yield load was 160 kN. The static test was first performed using

standard procedure as discussed above. Based on the load-displacement curve obtained

from the static test, the yield displacement was estimated for the cyclic loading scheme.

The pile was tested under cyclic loading until the pile failed.


The results of the vibration test showed that at the end of the forced vibration test,

the natural frequency of the 1.2-m pile (No.1) was slightly lower than that of 1.2-m pile

(No.2). Therefore, it was expected that the stiffness of pile No.2 was slightly larger than

that of pile No.1. The test arrangement was then prepared in such a way that pile No.1

was treated as a test pile and pile No.2 was treated as a reaction pile. The displacement at

the loading point of pile No.1 was initially used to control the testing. The yield load was

predicted as 2290 kN. Initially, the stiffness of pile No.1 was lower than No.2, as

expected. However, beyond 25 mm of the displacement of pile No.1, its stiffness became

higher than the other one. This was due to the fact that pile No.2 was located close to the

natural slope. Therefore the soil resistance at a large displacement level was lower due to

the smaller soil confining pressure. During the cyclic loading at 75% of displacement at

the yield load of pile No.1, there was a problem in controlling the actuator. The actuator

moved beyond the displacement target (i.e., 61 mm) by 20 mm causing considerable

movement to pile No.2 (i.e., 380 mm). The test was then immediately stopped and the

104

controlled location of displacement was switched from pile No.1 to pile No.2. Then, the

cyclic load test was continued until it reached the capacity of linear potentiometer.

4.5 Summary

A total of 5 instrumented CIDH piles with diameter varying between 0.4 m and

1.2 m were installed at the UCSD test site to study the pile diameter effect on the p-y

curves as well as the evaluate the effect of soil confinement in enhancing the inelastic

pile performance. The steel reinforcing of each pile consisted of 2% of longitudinal

reinforcement and 0.6% of transverse reinforcement. The amount of transverse

reinforcement used in this study is below that suggested in the BDS. Based on the

subsurface investigation results, the soil conditions at test site consisted of dense to very

dense weakly cemented sand without the presence of water table. Two types of testing

were conducted in this experimental study, including the vibration and full-scale lateral

load testing. The vibration tests consisted of ambient, impact, and forced vibration tests

with aiming at determining the dynamic properties of soil-pile system and utilizing the

test results to evaluate pile diameter effect at a very small strain level. This was

followed by the full-scale lateral load tests on CIDH piles under static and cyclic loadings.

The static load test results were used for back-calculating the p-y curves and evaluated

the pile diameter effect. The cyclic lateral load tests were carried out to investigate the

inelastic performance of CIDH piles. The test results of each test are presented in the

next chapter.

105

Table 4.1 Minimum Transverse Reinforcement Required by Bride Design Specifications (Caltrans 2000)

Pile Diameter, D (m)

fc’ (Mpa)

fy (Mpa)

ρs min

(%)

0.4 31.9 450 2.7

0.6 41.4 447 2.0

0.9 42.1 432 1.2

1.2 34.5 450 0.7

Note: Since fy for all sizes of pile diameter is more than 414 Mpa, the value of 414 Mpa was used to

determine the minimum transverse reinforcement. fc’ was obtained from compression tests on concrete

cylinders as summarized in Table 3.2.

Table 4.2 Summary of Average Concrete Strengths for CIDH Piles

Average Compressive Strength fc'(ave) (Mpa) Pile Diameter

(m) 7 days 28 days Test Day

Curing Time Corresponding to Test Day (days)

0.4 16.6 24.3 31.9 137

0.6 19.3 28.1 41.4 425

0.9 18.2 26.9 42.1 809

1.2 18.8 24.9 34.5 137

106

Table 4.3 Summary of Locations of Strain Gauges and Tiltmeters for Each Test Pile

Depth (m) Strain Gauge Tiltmeter

0.4-m Pile

0.6-m Pile

0.9-m Pile

1.2-m Piles

0.4-m Pile

0.6-m Pile

0.9-m Pile

1.2-m Piles

0.00

0.15

0.30

0.46

0.61

0.76

0.91

1.07

1.22

1.52

1.83

2.13

2.44

2.74

3.05

3.35

3.66

3.96

4.27

4.57

4.88

5.18

5.49

5.79

6.10

6.40

6.71

7.01

7.32

7.62

7.92

8.23

8.53

8.84

9.14

9.45

9.75

10.06

10.36

10.67

10.97

11.28

11.58

11.89

12.19

107


Date Descriptions Types of Vibration Testing

Ambient Impact Forced

0.4-m CIDH Pile

9/27/00 Undisturbed Soil Condition (Without Mass Shaker)

10/9/00 Undisturbed Soil Condition (With Mass Shaker)

Forced Vibration with Empty Bucket (0.65 kg)-Test 1

After Forced Vibration Test 1



10/10/00 Forced Vibration with Empty Bucket (0.65 kg)-Test 3




10/11/00 Forced Vibration with Empty Bucket (0.65 kg)-Test 5


10/13/00 Without Mass Shaker

108




0.6-m CIDH Pile



Forced Vibration with Empty Bucket (0.65 kg)-Test 1 11/5/99 Forced Vibration with Empty Bucket (0.65 kg)-Test 2-4

11/12/99 Forced Vibration with Empty Bucket (0.65 kg)-Test 5-13 11/17/99 Forced Vibration with One Plate (1.46 kg) -Test 1-6

Forced Vibration with Two Plates (2.06 kg) -Test 1-5 11/18/99 After Forced Vibration Test

Forced Vibration with Empty Bucket (0.65 kg) -Test 14 Forced Vibration with One Plate (1.46 kg) -Test 7 Forced Vibration with Two Plates (2.06 kg) - Test 6

12/7/99 Immediately After Lateral Load Test

Table 4. 6 Summary of Testing Program for Vibration Testing for 0.9-m CIDH Pile



0.9-m CIDH Pile


10/24/99 Forced Vibration with One Plate (1.46 kg) - Test 1 10/25/99 Forced Vibration with One Plate (1.46 kg) - Test 2-4 10/28/99 Forced Vibration with Full Bucket (2.65 kg)- Test 1-2

Forced Vibration with Empty Bucket (0.65 kg)-Test 1 11/4/99 After Forced Vibration Test

12/7/99 Immediately After Lateral Load Test

12/16/99 Forced Vibration with Full Bucket (2.65 kg)- Test 3-5

03/1/99 2.5 Months after Lateral Load Test

109

Table 4.7 Summary of Testing Program for Vibration Testing for 1.2-m CIDH Pile (No.1)



1.2-m CIDH Pile (No.1)



10/14/00 Forced Vibration with Empty Bucket (0.65 kg)- Test 1 Forced Vibration with Empty Bucket (0.65 kg)- Test 2 Forced Vibration with Empty Bucket (0.65 kg)- Test 3 After Forced Vibration Test 3

10/15/00 Forced Vibration with One Plate (1.46 kg) - Test 1 Forced Vibration with One Plate (1.46 kg) - Test 2 Forced Vibration with One Plate (1.46 kg) - Test 3 After Forced Vibration Test 3

Forced Vibration with Two Plates (2.06 kg) -Test 1 Forced Vibration with Two Plates (2.06 kg) -Test 2 Forced Vibration with Two Plates (2.06 kg) -Test 3 After Forced Vibration Test 3

Forced Vibration with Full Bucket (2.65 kg)- Test 1 Forced Vibration with Full Bucket (2.65 kg)- Test 2 Forced Vibration with Full Bucket (2.65 kg)- Test 3 After Forced Vibration Test 3

10/16/00 Forced Vibration with Two Plates (2.06 kg) Forced Vibration with One Plate (1.46 kg) Forced Vibration with Empty Bucket (0.65 kg)

10/17/00 Without Mass Shaker

110

Table 4.8 Summary of Testing Program for Vibration Testing for 1.2-m CIDH Pile (No.2)



1.2-m CIDH Pile (No.2)



10/17/00 Forced Vibration with Empty Bucket (0.65 kg)- Test 1 Forced Vibration with Empty Bucket (0.65 kg)- Test 2 Forced Vibration with Empty Bucket (0.65 kg)- Test 3 After Forced Vibration Test 3

Forced Vibration with One Plate (1.46 kg) - Test 1 Forced Vibration with One Plate (1.46 kg) - Test 2 Forced Vibration with One Plate (1.46 kg) - Test 3 After Forced Vibration Test 3

10/18/00 Forced Vibration with Two Plates (2.06 kg) -Test 1 Forced Vibration with Two Plates (2.06 kg) -Test 2 Forced Vibration with Two Plates (2.06 kg) -Test 3 After Forced Vibration Test 3

Forced Vibration with Full Bucket (2.65 kg)- Test 1 Forced Vibration with Full Bucket (2.65 kg)- Test 2 Forced Vibration with Full Bucket (2.65 kg)- Test 3 After Forced Vibration Test 3

Forced Vibration with Two Plates (2.06 kg) Forced Vibration with One Plate (1.46 kg) Forced Vibration with Empty Bucket (0.65 kg)

111

Figu

re 4

.1

Loca

tion

Map

of U

CSD

Eas

t Cam

pus T

est S

ite

UC

SD W

EST

CA

MPU

S

SITE

N

Gen

esee

Ave

.

UC

SD E

ast C

ampu

s

112

Figure 4.2 Topographic Map of UCSD East Campus Test Site

N

113

Figure 4.3 Geologic Map of UCSD East Campus Test Site (Elliot 1988)

GEOLOGIC MAP OF

UCSD EAST CAMPUS

Description Af = Artificial fill Qal = Quaternary alluvium Qls = Quaternary landslide deposit Qln = Linda Vista Formation Te = Scripps Formation

N

SITE

114

Figu

re 4

.4

Loca

tion

Map

of S

ubsu

rfac

e Ex

plor

atio

n

115

Figure 4.5 Soil Boring Log for Test Site (Borehole BH-1)

Project Number Boring Number

Logger Sheet of

Project ElevationLocation Water LevelsDrilling Method and Equipment Starting Date

Finishing Date

6"-6"-6" (N)

Silty SAND (SM), light brown with hematite stains, slightly moist, dense

12"9:40

9:05

9:109:15

9:20Driller says hit swelling layer @ 19' that blocked the hole

Silty SAND (SM), light to dark brown, moist, dense

S-5 7-44

12"

14"

18"

18" 13-21-18 (39)

12"

(6m)

10

(4m)

18"

18"

18"

8:55

8:5712-9-10 (19)

S-4

Silty SAND (SM), light brown with hematite stains, dry, medium dense

Clayey SAND (SC), dark brown, moist, dense

S-2 10-9-15 (24)

12-20-23 (43)

Depth of Casing, Drilling Rate, Drilling Fluid Loss, Tests and Instrumentation

Using Automatic Safety Hammer for SPT

Silty SAND (SM), light brown, dry, medium dense

18" S-3

S-1 Using SPT with Liners

Drilling Contractor

Sample Soil Description Comments

Dep

th B

elow

Su

rface

(ft)

Standard Penetration Test Results

Inte

rval

Num

ber a

nd

Type

Rec

over

y (ft

)

Soil Name, USCS Group Symbol, Color, Moisture Content, Relative Density or Consistency, Soil Structure, Mineralogy

Soil Boring Log

09/02/98 (8:30 AM)09/02/98 (7:50 PM)

Not encountered103.4 mCaltrans

East Campus Test SitePercussion Hammer

Tri County Drilling/ Dennis

T. Weaver

BH-1

1 3

SSRCA06

30

5

(2m)

(8m)

15

20

25

UC San Diego

116

Figure 4.5 Soil Boring Log for Test Site (Borehole BH-1, continued)


Logger Sheet of


Finishing Date

6"-6"-6" (N)

Using 50+ ft of Hex Rod for SPT, 2" Diameter Switching to Augers, cannot get percussion to penetrate 55 ft

0.4"

35

10m

12m

16m

14m 6"

6"

0.4"

SILTSTONE, grey with hematite stains, slightly moist6"

12:30

Clayey SAND (SC), light brown with hematite stains, slightly moist, very dense6"

11:17

60

S-6 518" 6"

S-7 45-8 (5.7")6"

With Liners

With Liners6"

9:50Clayey SAND (SC), light brown, slightly moist, very dense

Clayey SAND (SC), light brown with olive stains, slightly moist, very dense

T. Weaver

BH-1

2 3

SSRCA06

Soil Boring Log

09/02/98 (8:30 AM)09/02/98 (7:50 PM)



Tri County Drilling/ DennisDrilling Contractor


Dep

th B

elow

Su

rface

(ft)


Inte

rval

Num

ber a

nd

Type

Rec

over

y (ft

)



9:55

18m

4010"

Silty SAND (SM) with some rocks, light grey, slightly moist, very dense

S-10

S-8 52+

50S-9

45

50

55

6"

S-11

51

10:35

Clayey SAND (SC), light brown with olive and hematite stains, slightly moist, very dense

UC San Diego

117



Logger Sheet of


Finishing Date

6"-6"-6" (N)

Auger 40 ft, 4:3545ft, 4:5050ft, 5:00

S-12 50 Silty SAND (SM) grey, dry, very dense 6" 55ft, 5:10

60ft, 5:45

22m


24m

70

20m

Drilling Contractor


Dep

th B

elow

Su

rface

(ft)


Inte

rval

Num

ber a

nd

Type

Rec

over

y (ft

)


Soil Boring Log

09/02/98 (8:30 AM)09/02/98 (7:50 PM)




T. Weaver

BH-1

3 3

SSRCA06

Use Auger to Penetrate to Depth of 65 ft

75

80

85

90

26m

6"

65

UC San Diego

118

Figure 4.6 Soil Boring Log for Test Site (Borehole BH-2)


Logger Sheet of


Finishing Date

6"-6"-6" (N)

11" S-4

8:5512" S-5 8" Silty SAND (SM), light brown with some

black grains and hematite strains, slightly moist, very dense

11" 31-43 (5")

Silty SAND (SM), light brown with some black grains and hematite strains, slightly moist, very dense

30

5

(2m)

(8m)

15

20

25

T. Weaver

BH-2

1 3

SSRCA06

Soil Boring Log

09/03/98 (8:20 AM)09/03/98 (1:10 PM)



Tri County Drilling/ DennisDrilling Contractor


Dep

th B

elow

Su

rface

(ft)


Inte

rval

Num

ber a

nd

Type

Rec

over

y (ft

)



Clayey SAND (SC), light brown with hematite stains, dry, medium dense

Using Automatic Safety Hammer for SPT

8:216-8-10 (18)18" S-1 12"

8:2618"

(6m)

10

8:35

8:45

11"

(4m)

Silty SAND (SM), dark brown, slightly moist, medium dense

S-2 5-6-5 (11)18"

Silty SAND (SM), light brown with some black grains and hematite strains, slightly moist, very dense

10" 30-51(5")

S-3

UC San Diego

119



Logger Sheet of


Finishing Date

6"-6"-6" (N)

SILT with sand (ML), grey with hematite stains, slightly moist, hard

10:30

103.4 mNot encountered09/03/98 (8:20 AM)09/03/98 (1:10 PM)

Silty SAND (SM), light grey with some black grains and hematite strains, slightly moist, very dense

9:49

Sandy SILT (ML), grey with hematite stains, slightly moist, hard, flaky grains

Sandy SILT (ML), grey with hematite stains, slightly moist, hard ( found sand lense)

11" S-11 11" 20-51

6"

9:2212" S-7 12" 21-54 Silty SAND (SM), light grey with some

black grains and hematite strains, slightly moist, very dense (found lenses of grey siltstone near top of recovery)

9:35

27-50 (3")

10:02Silty SAND (SM) to SILT with sand (ML), reddish brown to grey with hematite stains, slightly moist, very dense

10:20

20-27-36 (63)

12-28-52 (5.5")

S-9

S-8 18"

17.5"

55

42-50S-10 11"

9:079" S-6

18"

17.5"

11"

45

50

Comments

Dep

th B

elow

Su

rface

(ft)


Inte

rval

Num

ber a

nd

Type

Rec

over

y (ft

)



Percussion HammerDrilling Contractor

Sample Soil Description


T. Weaver

BH-2

2 3

SSRCA06

Soil Boring Log

Caltrans East Campus Test Site

60

35

18m

40

10m

12m

16m

14m

UC San Diego

120



Logger Sheet of


Finishing Date

6"-6"-6" (N)

9" 9"

Clayey SAND (SC), brown with very little hematite stains, dry, very dense7" 6"

1:00

39-50

11-50S-15

12:10

11:20CLAY with sand (CL), greyish brown, slightly moist, hard

11:30

75

80

11:00

90

26m

65

85

15" S-13 15" 32-46-50 (3") Silty SAND (SM), reddish brown with hematite stains, slightly moist, very dense

S-12 52 Clayey SAND (SC), light brown with hematite stains, slightly moist, very dense

10:436"10:50

6"

T. Weaver

BH-2

3 3

SSRCA06

Drilling Contractor


Soil Boring Log

09/03/98 (8:20 AM)09/03/98 (1:10 PM)




Dep

th B

elow

Su

rface

(ft)


Inte

rval

Num

ber a

nd

Type

Rec

over

y (ft

)



24m

70

20m

22m

S-14

11:50

No Sample50 (6")0"6"

UC San Diego

121

Figu

re 4

.7

Soil

Con

ditio

n at

Tes

t Site

Incl

udin

g (a

) Cor

rect

ed S

PT-N

-Val

ues,

and

(b) S

hear

Wav

e V

eloc

ity P

rofil

e

302520151050Depth (m)

BH-1

BH-2

050

100

150

(N1) 6

0

020

040

060

0Sh

ear W

ave

Velo

city

(m/s

)

302520151050

Depth (m)Sh

ear W

ave

Vel

ocity

Trav

el T

ime

010

2030

4050

Trav

el T

ime

(ms)

315

m/s

560

m/s

(a)

(b)

122

F

igur

e 4.

8 A

dditi

onal

Loc

atio

ns o

f Soi

l Inv

estig

atio

n Ex

tract

ed fr

om A

vaila

ble

Soil

Rep

orts

Tes

t Site

Loca

tions

of S

oil I

nves

tigat

ion

B-1

= C

harte

r Sch

ool S

ite

B-2

= E

ast C

ampu

s U

tiliti

es P

lant

C

-1 =

UC

SD

Can

cer C

ente

r Bui

ldin

g C

-2 =

UC

SD

EB

U 3

and

4

C-3

= G

ilman

Driv

e P

arki

ng S

truct

ure

B-1

B-2

C-1

C-2

C-3

123

Figu

re 4

.9

Pile

Cro

ss S

ectio

n

124

0 2 4 6 8 10Strain (%)

0

200

400

600

800

Stre

ss (M

Pa)

0.6-m Pile(#3)

fyave = 447 MPa

Eave = 1.94x105 MPa

0 2 4 6 8 10Strain (%)

0

200

400

600

800

Stre

ss (M

Pa)

0.9-m Pile(#4)

fyave = 429 MPa

Eave = 1.94x105 MPa

0 2 4 6 8 10Strain (%)

0

200

400

600

800

Stre

ss (M

Pa)

0.6-m Pile(#7)

fyave = 434 MPa

Eave = 1.89x105 MPa

0 2 4 6 8 10Strain (%)

0

200

400

600

800

Stre

ss (M

Pa)

0.9-m Pile(#8)

fyave = 436 MPa

Eave = 1.86x105 MPa

Figure 4.10 Steel Stress-Strain Curves for 0.6-m and 0.9-m Piles

125

0 2 4 6 8 10Strain (%)

0

200

400

600

800

Stre

ss (M

Pa)

0.4-m Pile(#3)

fyave = 450 MPa

Eave = 1.80x105 MPa

0 2 4 6 8 10Strain (%)

0

200

400

600

800

Stre

ss (M

Pa)

1.2-m Pile(#5)

fyave = 450 MPa

Eave = 1.80x105 MPa

0 2 4 6 8 10Strain (%)

0

200

400

600

800

Stre

ss (M

Pa)

1.2-m Pile(#10)

fyave = 473 MPa

Eave = 2.20x105 MPa

Figure 4.11 Steel Stress- Strain Curves for 0.4-m and 1.2-m Piles

126

Drilling a Hole for CIDH Pile Installation

Installing Instrumented Steel Cage

Steel Cage in Place

Filling with Concrete

Figure 4.12 Sequence of CIDH Pile Installation

127

Figure 4.13 Construction of Reinforcement for Load Stub

Figure 4.14 Completion of Form Works for Load Stubs

128

Figure 4.15 Installation of Tiltmeters into Inclinometer Casing

129

Figu

re 4

.16

Loc

atio

ns o

f Cro

ssbo

w A

ccel

erom

eter

s for

the

0.4-

m a

nd 1

.2-m

CID

H P

iles i

n Fo

rced

Vib

ratio

n Te

st

130

Specifications

Voltage sensitivity 0.22 (1) mV/N (mV/lb) Frequency range 0.5 kHz Resonant frequency 2.7 kHz Linearity error < 2.0 % Amplitude range 0-22 kN

Physical Specifications

Mass 5.44 kg Head diameter 75 mm Tip diameter 75 mm Handle length 889 mm

Figure 4.17 Modal Hammer Used for Impact Vibration Test

131

Figure 4.18 Eccentric Mass Shaker

Figure 4.19 Aluminum Buckets with Two Aluminum Plates on Each of Them

132

0

5

10

15

20

25

0 10 20 30 40 50 60 70

Frequency (Hz)

Forc

e (k

N)

Empty Bucket (0.65 kg)

1 Aluminum Plate (1.46 kg)

2 Aluminum Plates (2.06 kg)

Full Bucket (2.65 kg)

Shaker Capacity = 22 kN

Figure 4.20 Relationship between Dynamic Force and Excitation Frequency for Different Masses of Aluminum Buckets

133

Figure 4.21 Modal Hammer Striking on Load Stub to Generate Initial Velocity to 0.6-m CIDH Pile for Impact Vibration Test

Figure 4.22 Mass Shaker Mounted on Top of Load Stub of 0.6-m CIDH Pile to Generate Harmonic Force Excitation to the Pile

134

Figure 4.23 Lateral Pile Load Test Sequence

0.6-m CIDH Pile

0.9-m CIDH Pile

N

0 5Scale (m)

Mobile DataAcquisition System

0.4-m CIDH Pile

Test No. 1

Test No. 2

Test No.3

1.2-m CIDH Pile (Pile No.1)

1.2-m CIDH Pile (Pile No.2)

Test No.4Hydraulic Actuator

135

Figure 4.24 Lateral Load Test Set-up and Locations of Instruments (Test No.1)

0.6-m Dia. CIDH Pile0.9-m Dia. CIDH Pile

Linear Potentiometer

0.25 m0.25 m

Strain Gauge on Longitudinal Bar

Strain Gauge on Spiral

Tiltmeter


0

1

3

4

6

7

9

10

12

Hydraulic Actuator

0.84 m

0.25 m0.25 m

0.84 m

2

5

8

11

ReferencePost

A B, D C AB, DC

136


0.9-m CIDH Pile1.2-m CIDH Pile

(Pile No.1)

0.30 m

Strain Gauge on Longitudinal Bar Tiltmeter


Hydraulic Actuator

0.42 m

0.30 m

0.67m

0.13 m0.15 m

ABB A,C D

0

1

3

4

6

7

9

10

12

2

5

8

11


ReferencePost

137


1.2-m CIDH Pile(Pile No.1)0.4-m CIDH Pile

0.30 m



Hydraulic Actuator

0.39 m

0.10 m

ABCD

0

1

3

4

6

7

9

10

12

2

5

8

11


ReferencePost

138


1.2-m CIDH Pile(Pile No.1)

Linear Potentiometers

Linear Potentiometers

0.30 m



Hydraulic Actuator

0.64 m

0.30 m

0.82 m

0.13 m0.19 m

ABCD

1.2-m CIDH Pile(Pile No.2)

ReferencePost

0

1

3

4

6

7

9

10

12

2

5

8

11

ABCD

139

Figure 4.28 Test Setup for Lateral Load Test No.1

Figure 4.29 UCSD Data Acquisition System

140

This page is intentionally blank.

141

Chapter 5 TEST RESULTS

In this chapter, the test results from vibration and lateral load testing are presented.

The first section presents the results from vibration testing, which includes the natural

frequency, damping ratio, and mode shape of the soil-pile system. The second section

provides the results from full-scale lateral load tests. The static and cyclic load-

displacement curves of each pile together with strain gauge data are given. A brief

description of pile damage and photographs are also provided. At the end of this section,

the test results are discussed in specific topics, including the location of maximum

moment and inelastic performance of CIDH piles.

5.1 Vibration Testing

The results from three types of vibration tests (i.e., ambient, impact, and forced

vibration tests) are presented in this section. The natural frequencies of the soil-pile

systems obtained from different types of vibration tests are compared and discussed.

This is followed by the results and discussions on the system damping ratio. Finally, the

mode shapes of individual soil-pile systems derived from the strain gauge and

accelerometer data are presented.

5.1.1 Natural Frequency

5.1.1.1 Ambient Vibration Test

The tests results obtained from both N-S and E-W directions are essentially the

same; therefore, only the results for E-W direction are presents in the plots. Figure 5.1

through Figure 5.3 present the power spectrum from ambient vibration tests for the 0.4-m,

0.6-m and 0.9-m CIDH piles, respectively. The power spectrums presented in the plots

were directly obtained from the signal analyzer, which allows the user to simply process

the data in both time and frequency domain during the test. The plots represent the

amplitude of acceleration in frequency domain before and after harmonic forced vibration

142

tests. The highest peak of acceleration represents the fundamental natural frequency of

the soil-pile system. The results from the 1.2-m CIDH pile are not presented herein

because the peak of the natural frequency of the soil-pile system could not be observed as

shown in Figure 5.4. This is due to the fact that the pile had a very large stiffness;

therefore, its vibration was so small that the amplitude of vibration was approximately

noise level.

In general, the test results show that the natural frequency of the system decreases

with increasing the degree of soil disturbance (i.e. the natural frequency of the system

after conducting the forced vibration test was less than that of the undisturbed soil

condition). Figure 5.2 shows that after lateral load test No.1 (i.e., 0.6-m pile vs. 0.9-m

pile), the natural frequency of the 0.6-m pile significantly decreases from about 15 Hz to

3 Hz due to the degradation of pile integrity, with the pile reaching the failure at the end

of the test. Figure 5.3 shows that the natural frequency of the 0.9-m pile before and after

the lateral load test decreases from 25.4 Hz to 17.5 Hz. This is due to the fact that the

force acting on the pile during the lateral load test caused the development of a gap

deeper into the ground. As a result, the free standing length of the pile was longer and

therefore lowered the system’s stiffness. However, approximately 2.5 months after the

test, the gapping of the soil surrounding the pile disappeared due to the rain and other

environmental factors. The natural frequency of the system was then measured again.

The natural frequency of the system was nearly fully recovered as presented in Figure 5.3.

Figure 5.4 presents a comparison of the power spectrums of all pile diameters for the

undisturbed soil condition. As expected, the natural frequency of the of the system

increases with increasing the pile stiffness (i.e., pile diameter). A summary of natural

frequencies obtained from ambient vibration tests is given in Table 5.1.


The Frequency Response Function (FRF) of each pile obtained from the impact

vibration test is presented in Figure 5.5 through Figure 5.9, which corresponds to the ratio

143

of the pile acceleration to the force applied using a modal hammer. Figure 5.10 presents

the FRF of all piles in the same plots. The results from ambient and impact vibration

tests are reasonably in good agreement. However, the natural frequency based on the

impact vibration tests is better defined due to a higher amplitude of excitation. The

natural frequency of the 1.2-m pile could be determined using the impact vibration test

whereas this was not possible by means of the ambient vibration test. Similar findings as

the ambient vibration tests were obtained. A summary of natural frequencies obtained

from impact vibration tests is provided in Table 5.1.


Figure 5.11 through Figure 5.19 present the frequency response curves for each

pile obtained from forced vibration tests at different levels of amplitude of shaking. The

excitation force (F = mω2r) is not constant. It is a function of the mass of the bucket, m,

the angular frequency, ω, and the radius to center of gravity of mass, r. For a given

bucket (i.e., m and r = constant), the amplitude of acceleration depends on the square of

angular frequency. Therefore, in order to consider the response due to the constant

dynamic force throughout the frequency response curve, the measured acceleration, a, on

the y-axis, was normalized by ω2. The peaks in the response curves represent the natural

frequency of the system. Figure 5.11 and Figure 5.12 shows that there are two peaks in

the response curves. The first peak represents the natural frequency of the translation

mode. The second peak represents the natural frequency due to rocking caused by the

unexpected loosening of the motor of the shaker during the testing. This explanation was

obtained from the filed observation on the motor of the shaker at the end of the last test

on the 0.4-m pile, as well as the results from the impact vibration tests. The results from

the impact vibration tests show that this rocking mode was not observed either before the

shaking where the motor was still completely fixed to the shaker or when the shaker was

removed but existed at the end of the forced vibration as presented in Figure 5.5 and

Figure 5.6.

144

It can be observed that the natural frequencies obtained from forced vibration test

are somewhat lower than those obtained from ambient and impact vibration tests. The

excitation force produced by the shaker was large enough to form a small gapping around

the pile resulting in lowering the system stiffness, and consequently reducing the system

natural frequency. The natural frequency of the system depends on the level of excitation

force and the number of test runs. Figure 5.16 presents frequency response curves for

the1.2-m pile (No.1) at different levels of horizontal excitation force. Considering at the

same force level, the natural frequency of the system progressively drops between the

initial and the final sweep tests. The natural frequency tends to be constant with

increasing number of sweep tests because the gap length was stabilized (i.e., shakedown

effect). In addition, as the amplitude of excitation force increases, the natural frequency

of system decreases. This might be due to two possible reasons: 1) the pile becomes

nonlinear as the amplitude of the excitation increased and/or 2) the gap length increases

with excitation force. In order to verify this, at the end of the sweep tests with the pile

experiencing the maximum level of excitation force, additional sweep tests were

performed at lower amplitudes of excitation force. By doing this, the gap length or the

free standing height of the pile remained unchanged. If the decrease in natural frequency

was due to the pile nonlinearity, lowering the amplitude of shaking would increase the

natural frequency of the system. In fact, the test results for the 1.2-m pile (No.1) in

Figure 5.17 indicates that the natural frequency of the system remained the same even

though the amplitude of shaking changed, inferring that the decrease in natural frequency

was essentially due to the growth of the gap length with amplitude of shaking (i.e., free

standing height increased with amplitude of shaking). Similar results were observed for

the other pile diameters as presented in Figure 5.13, Figure 5.15, and Figure 5.19. Figure

5.20 presents a comparison of response curves for different pile diameters which shows

that the natural frequency of the system increases with an increase of pile diameter.

Table 5.2 summarizes the natural frequencies of individual piles obtained from forced

vibration tests.

145

5.1.2 Damping Ratio


Figure 5.21 presents the typical acceleration response of each pile under free

vibration obtained from impact vibration tests. As expected, the motion of the piles

decays with time. This decay is more rapid for the larger pile relative to the smaller pile.

Based on these decayed curves, the damping ratios were estimated using the logarithmic

decrement method. The damping values were also obtained by the method of half-power

bandwidth of the Frequency Response Function peaks. The damping ratios based on both

methods are in good agreement. The damping ratio varies with pile diameter from

approximately 3% for the 0.4-m pile to about 25% for the 1.2-m pile as summarized in

Table 5.3. The results indicate that motion in the larger pile decays more rapid than that

of the smaller one. The damping of the system is mainly attributed to radiation damping

because material or hysteretic damping is negligible in small strain testing (i.e. impact

test). The radiation damping, associated with energy carried away from the foundation

by stress waves traveling in the soil, is a function of contact area and excitation frequency

(Dobry and Gazetas 1985). For that reason, as the pile diameter becomes larger, the

excitation frequency and contact area increase, and consequently increasing the damping

of the system.


Table 5.2 summarizes damping ratios of the system for each pile obtained from

forced vibration testing by using the half-power bandwidth method. Considering the

same pile diameter, the damping ratios obtained from the forced vibration tests were

generally lower than those obtained from impact test as presented in Figure 5.22. It

should be noted that for impact vibration test, only damping ratio under undisturbed soil

condition were plotted the figure. One possible explanation regarding the lower damping

ratio obtained from the forced vibration is that a formation of gapping caused by forced

146

vibration tests decreased the amount of energy that could be carried away from the

foundation, consequently decreasing the overall damping ratio of the system. The

damping ratios varied from approximately 1% for the 0.4-m pile to about 24% for the

1.2-m pile.

Figure 5.23 presents the relationship between damping ratio of the system and the

mass of the bucket, which directly relates to the amplitude of excitation force. For the

1.2-m pile (No.1), the damping ratio appears to decrease with increasing amplitude of

excitation force probably due to the growth of gap length, which reduces the radiation

damping. However, this is not consistent for the other diameters for which the damping

ratios are much smaller than those of the 1.2-m pile. Two possible reasons can be

explained. First, for the smaller pile, the hysteretic damping that increases with force

level becomes more predominant and may increase the overall damping of the system

even though the radiation damping decreases with the amplitude of shaking. Second, a

small error in the measurement of acceleration could significantly cause inaccuracy in the

estimation of damping ratio using the half-power bandwidth method.

5.1.3 Mode Shape

The mode shapes of each pile were estimated based on data from a series of strain

gauges (S.G.) and/or accelerometers (Acc.) along the piles depending on which types of

data were available. It should be noted that for the 0.6-m and 0.9-m piles, accelerometers

were not installed along the length of the pile; therefore, only strain gauge data was

available. In addition, since the stiffness of the 1.2-m pile was very high, the response of

strain gauges due to the dynamic force was insignificant, and therefore the mode shape

was obtained using accelerometer data only. To determine mode shape from strain gauge

data, pile curvatures were first calculated, and then the 6th order polynomial function was

fit to the discrete curvature data. Subsequently, the displacement of the pile representing

its mode shape was determined by double integration of the curvature function. Figure

5.24 presents mode shapes of each pile based on its resonant frequency at the maximum

147

level of excitation force plotted in terms of normalized amplitude with a ratio of unity at

the pile head. The mode shapes of the 0.4-m pile obtained from both strain gauge and

accelerometer data were in good agreement. The results from the mode shape confirm

that the pile stiffness increases with pile diameter, as is expected. Furthermore, the depth

of zero displacement related to the effective pile length increases with pile diameter.

5.2 Lateral Load Testing

In this section the individual lateral load test results are presented starting from

lateral load test No.1 to lateral load test No.4. The load-displacement curves subjected to

both static and cyclic loading are presented. The responses of bending strain gauges at

different load levels are also given. Furthermore, brief descriptions of the observed

failure of the piles, together with photographs are provided.

5.2.1 Lateral Load Test No. 1

5.2.1.1 Load-Displacement Curves

The 0.6-m CIDH pile was tested under both static and cyclic loading using the

0.9-m CIDH pile as the reaction. Load-displacement curves under static loading for the

0.6-m and 0.9-m CIDH piles are presented in Figure 5.25. For a purpose of comparison,

the load-displacement curve of the 0.9-m pile from lateral load test No.2 is also presented

in Figure 5.23. The load-displacement curve of the 0.9-m pile obtained from test No.2 is

somewhat lower than that obtained from test No.1. Two possible reasons can be

explained. First, the soil conditions at different periods of time might be different. The

soil condition in Phase I was observed to be relatively dry, whereas that in Phase II might

be slightly moist, due to a rain about a week before the test which possibly softened the

soil. Second, there might be a human error in the calibration factor of the actuator load

by a certain factor. Multiplying the load obtained from the Phase I by a factor of 0.75

yields an excellent agreement with the results from Phase II as presented in Figure 5.26.

148

It was believed that the second reason is more likely due to the following reasons: 1). The

results from the ambient and impact vibration tests on the 0.9-m pile indicated that the

system natural frequency during Phase I and before Phase II were almost identical

indicated that the system stiffness at two different periods of time were very similar. 2).

The back-calculated p-y curves of the 0.6-m pile using the uncorrected load-displacement

curves from Phase I yielded significant too large resistance when compared to back-

calculated p-y curves from the larger pile diameters which appeared to be unreasonable.

Based on this information, the load-displacement curves of the 0.6-m pile which was

carried out in Phase I was reduced by multiplying with a constant of 0.75 to correct for

the human error. The load-displacement curves under static loading for the 0.6-m and

0.9-m CIDH piles after applying the correction factor are presented in Figure 5.27. The

load-displacement curve under cyclic loading of the 0.6-m CIDH pile after applying the

correction factor is shown in Figure 5.28.

The load-displacement curve under cyclic loading is an inverted S-shape, which

indicates the effect of soil gapping. Using the equivalent elasto-plastic load-displacement

relationship, yield displacement can be estimated by extrapolating the elastic response

(i.e., first yield of the steel) to the maximum load and therefore the displacement ductility

for each displacement level can be obtained (Priestley et al. 1996). The estimated yield

displacement was 40 mm. The test pile has displacement ductility of 7.4 and it failed at

the first cycle of displacement ductility of 8.1.

5.2.1.2 Longitudinal Strain Gauge Data

The responses of strain gauges at different levels of loading are presented in

Figure 5.29. Strain gauge data indicates that the location of maximum moment occurs at

depth about 0.9 m corresponding to 1.5D. No significant strains were measured in the

longitudinal bars below a depth of 3.6 m (6D). It is noted that all of the strain gauges

were damaged during cyclic loading due to the breaking of strain gauge leads at the

vicinity of plastic hinge.

149

5.2.1.3 Transverse Strain Gauge Data

The transverse strain profiles in various directions as presented in Figure 5.30

indicate that the both confining steel strains (A and C) as well as shear steel strains (B

and D) are insignificant compared to the longitudinal strain. The confining steel strain in

the compression side has a similar shape as that observed in the compression rebar. The

shear strain on the other hand shows that they are insignificant at all depths. This is

because the shear capacity of the reinforcement pile is much larger than that the shear

demand and hence the shear force in the pile is taken by the concrete.

5.2.1.4 Observed Pile Performance

At a ground displacement of 25.4 mm (48 mm at load point), the occurrence of

hair line cracks on the column was observed. During the cyclic loading at 152 mm

ground displacement (295 mm at load point equivalent to displacement ductility of 7.4),

the concrete started spalling. Rupture of the steel spiral was observed at a depth of 0.3 m

below the ground surface during the first cycle with a displacement at a load point of 325

mm (displacement ductility of 8.1). This was followed with three longitudinal rebars at a

depth of about 0.3 m in the A direction (Figure 5.31) and then two longitudinal rebars at

the same depth in the C direction (Figure 5.32). There were a total of 5 broken

longitudinal rebars in the direction of the loading application. After the completion of the

test, the soil around the test pile was excavated to investigate the plastic hinge location

and the pattern of cracks along the pile. Figure 5.33 and Figure 5.34 present the crack

pattern along the pile. There was severe damage on the pile between the depths of 0 m

and 0.6 m. The crack pattern apparently occurred at 89 mm intervals corresponding to

the spacing of the spiral. The crack width appeared to be smaller at the deeper depth.

The cracks become insignificant at a depth greater than 1.8 m below the ground surface.

150



For lateral load test No.2, the load-displacement curves under static loading for

the 0.9-m and 1.2-m CIDH piles are presented in Figure 5.35. The load-displacement

curve under cyclic loading of the 0.9-m CIDH pile is shown in Figure 5.36. Similar to

the previous test, the shape of the load-displacement curve is an inverted S-shape

indicating the effect of soil gapping. The displacement at yield was estimated as 57 mm.

It is noted that the displacement in the pull direction could not reach the target due to the

pulling limit capacity of the actuator at 980 kN. The pile was laterally loaded until it

reached the capacity of the linear potentiometer; the test was then stopped without failing

the pile. The maximum displacement at the end of the test corresponded to a

displacement ductility of 8.7.


The responses of strain gauges at different levels of loading are presented in

Figure 5.37. The location of maximum strain corresponding to the maximum moment

occurred at a depth of 2.1 m (2.33D). No significant strains were measured in the

longitudinal bars below a depth of 4.8 m corresponding to 5.33D.


Cracks were noticed along the 0.9-m CIDH pile starting from the depth of 0 to

about 2.4 m, which was corresponding to the maximum depth that we could excavate

using a backhoe. Severe cracks were observed between depths of 0.9 m and 2.4 m

related to the vicinity of the location of maximum moment. Figure 5.38 shows the crack

patterns along the 0.9-m CIDH pile.

151



For lateral load test No.3, the load-displacement curves under static loading of the

0.4-m CIDH pile is presented in Figure 5.39. The load-displacement curve for the 0.4-m

CIDH piles under cyclic loading showing the effect of gapping is presented in Figure

5.40. The yield displacement was estimated as 35 mm for computing the displacement

ductility of the pile. The pile performed well under cyclic loading up to a displacement

ductility of 5.8 and it failed at a displacement ductility of 6.9.


The strain gauge data (Figure 5.41) shows that the location of maximum moment

occurred at a depth of about 0.60 m corresponding to 1.50D. No significant strains were

measured in the longitudinal bars below a depth of 2.4 m (6.0D).


At a load of 165 kN, hair line cracks along the column were observed. The cracks

of the pile just below the ground surface were observed during the cyclic loading at a

displacement at the load point of 61 mm (displacement ductility of 1.74). Spalling of

concrete occurred when the pile was loaded at a displacement of 203 mm (displacement

ductility of 5.8). Three of longitudinal reinforcing bars were broken at a depth of 0.3 m

during the first cycle at a displacement of 244 mm (displacement ductility of 6.9). Figure

5.42 showed the rupture of the reinforcing steels at a depth of 0.3 m below the ground.

Figure 5.43 shows the patterns of crack along the 0.4-m CIDH pile. No crack was

observed below a depth of 1.2 m.

152



Load-displacement curves of the 1.2-m CIDH piles under static and cyclic loading

are presented in Figure 5.44 and Figure 5.45, respectively. The yield displacement was

estimated as 75 mm. As described earlier in the test setup section, Pile No.2 moved more

than the displacement target to a displacement of 380 mm due to a problem in controlling

the actuator. The pile was then unloaded to zero and the controlled displacement was

changed from Pile No.1 to Pile No. 2. The cyclic load test continued to load for 3 cycles

at displacement ductilities of 4.1, 5.2 and 6.2. Though the pile did not reach failure, the

test was stopped because it reached the capacity of the linear potentiometers. Similar to

test No.2, the displacement in the pull direction was limited by the capacity of the

actuators at 1960 kN (2 actuators).


The strain gauge data presented in Figure 5.46 and Figure 5.47 indicate that the

location of maximum moment occurs at a depth of 3.0 m corresponding to 2.5D. No

significant strains were measured in the longitudinal bars below a depth of 6.40 m

(5.33D).


There was no sign of pile damage throughout the test. However, after the

excavation, some cracks were observed on Pile No.2 between the depths of 0.75 m and

4.5 m as presented in Figure 5.48. There was no damage on Pile No.1.

153

5.2.5 Comparison of Location of Maximum Moment

The depth of the maximum moment, or the plastic hinge, is one important

parameter used in the design of pile under lateral loading. The depth of the plastic hinge

depends on the stiffnesses of the soil and pile, as well as the height above ground (Budek,

1997). Typical values assumed in design, based on the design chart developed by Budek

(1997), range from 0.5D to 2.0D. The strain profile based on the test data at

approximately the yield load of each pile were plotted against the ratio of depth to pile

diameter, D, in the same plot as presented in Figure 5.49. The results show that the depth

of the plastic hinge ranges from about 1.0D to 3.0D, which are in reasonable agreement

with the Budek design chart (Budek 1997). It appears that this ratio tends to increase

with the pile diameter, which is not considered in the current design. Another interesting

observation in this plot is that the depth of zero moment occurs at approximately 6D for

all pile diameters. Below this depth the moment is insignificant.

5.2.6 Observed Inelastic Behavior of CIDH Piles

The amount of transverse reinforcement based on the specification suggested by

BDS 1993 appears to be conservative for the design of CIDH piles because this amount

of transverse reinforcement was recommended based on the test results of columns.

However, in case of the piles, the confinement from the surrounding soil can

considerably enhance the inelastic behavior of the pile. Budek (1997) studied the effect

of external confinement in improving the inelastic behavior of the CIDH pile by

conducting the experiments on CIDH piles with external confinement provided by a

series of saddles with the rubber to model confinement from the soil. Budek showed that

an adequate seismic performance of CIDH piles can be achieved with only the moderate

levels of transverse reinforcement due to the effect of external confinement.

Figure 5.50 show the cyclic load-displacement curves of each pile tested until its

failure or until the actuator reached its displacement limit. The test results indicate that

154

all the test piles have ductile behavior with a displacement ductility of more than 5, even

though only low to moderate level of transverse reinforcement of 0.6% was used. This

indicates that the equation in the BDS may be conservative in determining the amount of

transverse reinforcement in the pile. These test results of CIDH piles in real soil support

the finding of a recent research (Budek, 1997). Therefore, the effect of soil confinement,

which can reduce the amount of transverse reinforcement, should be considered to

incorporate in the future seismic design of CIDH piles, which results in a decrease in the

construction cost of deep foundations. The analyses on the effect of soil confinement on

the inelastic behavior of the pile are presented in the next chapter.

Based on Figure 5.50, some of interesting behavior of CIDH piles observed from

the load-displacement curves can be noted as the followings:

• The strength degradation of the first cycle is significantly greater than the

subsequent cycles.

• The displacement ductility of the pile appears to increase as the pile diameter

increases.

• The cyclic load-displacement curves are similar to the inverted S-shape, which

indicates the effect of gapping. The stiffness of soil-pile system is quite low when

the pile displacement is less than the gap width. However, the stiffness becomes

stiffer as the pile starts to have a contact with the soil.

• Pile capacity in the pull direction is slightly greater than the push direction,

probably due to the effect of interaction between the test pile and reaction pile.

• Hysteretic damping increases as the displacement of the pile increases.

5.3 Summary

The test results from the vibration and lateral load tests for various pile diameters

have been presented and some interpretation of the test data has been provided. The

results from vibration testing show that the natural frequency of the soil-pile system

155

increases as the pile diameter increases due to the increase of soil-pile system stiffness.

The natural frequencies obtained from both ambient and impact vibration tests are similar,

whereas those obtained from the forced vibration tests are somewhat smaller because the

development of small gapping occurred due to the dynamic force from the shaker,

resulting in increasing the free standing height and decreasing the system stiffness. The

damping ratio increases as the pile diameter increases due to the effect of radiation

damping which is a function of the contact area and the frequency excitation.

The characteristics of cyclic load-displacement curves as the inverted S-shape

indicate the effect of gapping. All of the piles show sufficient inelastic performance with

the displacement ductility of more than 5, even though the smaller amount of transverse

reinforcement than that suggested by BDS was used. The strain gauge results indicate

that the maximum moment occurred at depths approximately 1.0D to 3.0D which

generally agree with the typical values used in design (Budek 1997). Furthermore, the

depth of zero moment of all pile is approximately 6D.

156

Table 5.1 Summary of Natural Frequencies of Soil-Pile Systems from Ambient and Impact Vibration Tests

Pile Descriptions Natural Frequency (Hz)

Diameter Ambient Impact E-W N-S E-W N-S

0.4 m Without Mass Shaker 13.6 13.9 13.4 13.7 With Mass Shaker 12.6 12.9 12.3 12.7 After Forced Vibration (Test 1) 11.4 11.4 10.6 11.3 After Forced Vibration (Test 2) 11.1 11.3 10.3 11.1 After Forced Vibration (Test 3) 11.0 11.3 10.1 10.9 After Forced Vibration (Test 4) 10.9 11.3 10.0 10.8 After Forced Vibration (Test 5) 10.6 11.3 9.8 10.8 Without Mass Shaker 12.1 12.3 11.6 11.8

0.6 m Without Mass Shaker 18.8 18.8 18.0 18.2 With Mass Shaker 17.0 17.0 16.5 16.8 After Forced Vibration 14.9 15.0 13.3 13.6 Immediately After Lateral Load Test 3.8 2.3 3.1 1.8

0.9 m With Mass Shaker 25.4 - 25.4 26.3 After Forced Vibration 24.4 - 23.3 24.7 Immediately After Lateral Load Test 17.5 16.5 15.8 15.1 2.5 Months after Lateral Load Test 24.1 24.1 24.0 24.0

1.2 m Without Mass Shaker - - 34.5 34.5 (Pile No.1) With Mass Shaker - - 33.6 33.4

After Forced Vibration (Rotation Mass = 0.65 kg) - - 32.9 31.5 After Forced Vibration (Rotation Mass = 1.46 kg) - - 31.2 29.6 After Forced Vibration (Rotation Mass = 2.06 kg) - - 28.0 26.5 After Forced Vibration (Rotation Mass = 2.65 kg) - - 26.5 25.1 Without Mass Shaker - - 31.5 29.0

1.2 m Without Mass Shaker - - 31.8 33.0 (Pile No.2) With Mass Shaker - - 31.8 32.3

After Forced Vibration (Rotation Mass = 0.65 kg) - - 32.3 32.0 After Forced Vibration (Rotation Mass = 1.46 kg) - - 32.0 32.0 After Forced Vibration (Rotation Mass = 2.06 kg) - - 31.2 32.0 After Forced Vibration (Rotation Mass = 2.65 kg) - - 31.2 31.5

157

Table 5.2 Summary of Natural Frequencies and Damping Ratios of Soil-Pile Systems from Forced Vibration Tests

Pile Diameter (m)

Mass (kg)

Run Number

Natural Frequency (Hz)

Damping Ratio (%) Remarks

0.4 0.65 1 10.2 1.2 0.65 2 9.3 1.4 0.65 3 9.2 1.1 0.65 4 9.1 1.9 0.65 5 8.7 1.8 Raining

0.6 0.65 1 13.7 2.9 0.65 2 13.2 2.5 0.65 3 13.0 2.4 1.46 1 12.1 2.2 1.46 2 11.6 2.2 1.46 3 11.4 2.8 2.06 1 11.2 2.9 2.06 2 11.0 2.9 2.06 3 11.0 3.1 2.06 4 11.0 3.3 1.46 4 10.8 3.1 0.65 4 10.8 3.7

0.9 1.46 1 17.9 5.2 1.46 2 18.0 4.6 1.46 3 18.0 4.9 2.65 1 17.0 3.5 2.65 2 16.7 5.8 0.65 1 16.9 5.4 2.06 1 12.9 6.0 After Lateral Load Test 2.06 2 12.9 6.0 After Lateral Load Test

1.2 (Pile No.1) 0.65 1 28.3 21.1 0.65 2 28.3 23.6 0.65 3 28.3 23.6 1.46 1 26.3 17.5 1.46 2 24.6 20.2 1.46 3 24.6 20.2 2.06 1 23.8 17.1 2.06 2 21.8 15.4 2.06 3 21.8 15.8 2.65 1 21.5 14.1 2.65 2 21.3 16.1 2.65 3 21.2 16.1 2.06 4 21.0 14.8 1.46 4 20.8 10.9 0.65 4 20.8 8.2

1.2 (Pile No.2) 0.65 1 29.3 -- 0.65 2 29.3 -- 0.65 3 29.3 -- 1.46 1 28.0 -- 1.46 2 27.6 -- 1.46 3 27.6 -- 2.06 1 27.3 -- 2.06 2 27.2 -- 2.06 3 27.2 -- 2.65 1 26.7 -- 2.65 2 26.5 -- 2.65 3 26.5 -- 2.06 4 26.5 -- 1.46 4 26.5 -- 0.65 4 26.5 --

158

Table 5.3 Summary of Damping Ratios of Soil-Pile Systems from Impact Vibration Tests

Pile Descriptions Damping Ratio (%)

Diameter Logarithmic Decrement

Half-Power Bandwidth

E-W N-S E-W N-S 0.4 m Without Mass Shaker 2.8 2.8 2.6 3.0

With Mass Shaker 3.2 2.8 3.0 3.3 After Forced Vibration (Test 1) - - 4.5 5.1 After Forced Vibration (Test 2) 6.2 6.6 4.4 5.1 After Forced Vibration (Test 3) 5.7 4.1 4.0 2.7 After Forced Vibration (Test 4) 5.2 4.3 4.3 3.1 After Forced Vibration (Test 5) 5.1 4.3 4.5 3.0 Without Mass Shaker 3.8 3.5 3.9 4.6

0.6 m Without Mass Shaker 4.6 4.5 4.9 5.6 With Mass Shaker 3.8 3.9 3.8 3.6 After Forced Vibration 5.6 5.1 5.7 5.7 Immediately After Lateral Load Test 4.3 4.4 5.3 6.1

0.9 m With Mass Shaker 8.6 9.9 9.1 10.8 After Forced Vibration 7.3 7.7 7.0 7.6 Immediately After Lateral Load Test 5.7 5.9 6.5 6.6 2.5 Months after Lateral Load Test - - 9.1 11.5

1.2 m Without Mass Shaker 21.4 23.2 22.5 29.9 (Pile No.1) With Mass Shaker 21.9 24.1 22.3 29.6

After Forced Vibration (Rotation Mass = 0.65 kg) 21.3 20.9 18.2 24.6 After Forced Vibration (Rotation Mass = 1.46 kg) 19.2 18.3 18.9 20.7 After Forced Vibration (Rotation Mass = 2.06 kg) 18.2 15.5 19.2 18.2 After Forced Vibration (Rotation Mass = 2.65 kg) 17.4 15.8 18.2 15.7 Without Mass Shaker 20.9 17.8 17.3 18.6

1.2 m Without Mass Shaker 24.7 - 24.7 - (Pile No.2) With Mass Shaker 24.9 - 24.4 -

After Forced Vibration (Rotation Mass = 0.65 kg) - - 22.9 - After Forced Vibration (Rotation Mass = 1.46 kg) - - 24.1 - After Forced Vibration (Rotation Mass = 2.06 kg) - - 24.5 - After Forced Vibration (Rotation Mass = 2.65 kg) - - 24.6 -

159

0 5 10 15 20 25 30Frequency (Hz)

0.001

0.01

0.1

1

10

Nor

mal

ized

Acc

eler

atio

n

without shaker (undisturbed soil)with shaker (undisturbed soil)after forced vibration test 1after forced vibration test 5after forced vibration (w/o shaker)

N

Shaking Direction

Figure 5.1 Power Spectra for 0.4-m CIDH Pile from Ambient Vibration Tests (E-W Direction)

0 5 10 15 20 25 30 35Frequency (Hz)

0.01

0.1

1

10

Nor

mal

ized

Acc

eler

atio

n

without shaker (undisturbed soil)with shaker (undisturbed soil)after forced vibration testimmediately after lateral load test

N

Shaking Direction


160

0 10 20 30 40 50Frequency (Hz)

0.01

0.1

1

10

Nor

mal

ized

Acc

eler

atio

n

with shaker (undisturbed soil)after forced vibration testimmediately after lateral load test2.5 months after lateral load test

N

Shaking Direction


0 10 20 30 40 50Frequency (Hz)

0.001

0.01

0.1

1

10

Nor

mal

ized

Acc

eler

atio

n

0.4-m0.6-m0.9-m+mass1.2-m (No.1)

Figure 5.4 Comparison of Power Spectra for Various Pile Diameters from Ambient Vibration Tests (E-W Direction)

161

0 5 10 15 20 25 30Frequency (Hz)

0

0.5

1

1.5

2

2.5

3

Am

plitu

de (g

/N)

without shaker (undisturbed soil)with shaker (undisturbed soil)after forced vibration test 1after forced vibration test 5after forced vibration (w/o shaker)

N

Shaking Direction

Figure 5.5 Frequency Response Functions for 0.4-m CIDH Pile from Impact Vibration Tests (E-W Direction)

0 5 10 15 20 25 30 35Frequency (Hz)

0

0.5

1

1.5

2

Am

plitu

de (g

/N)

with shaker (undisturbed soil)after forced vibration testimmediately after lateral load testwithout shaker (undisturbed soil)

N

Shaking Direction


162

0 10 20 30 40 50Frequency (Hz)

0

0.2

0.4

0.6

0.8

1

Am

plitu

de (g

/N)

with shaker (undisturbed soil)after forced vibration testimmediately after lateral load test2.5 months after lateral load test

N

Shaking Direction


0 10 20 30 40 50Frequency (Hz)

0

0.1

0.2

0.3

0.4

0.5

Am

plitu

de (g

/N)

without shaker (undisturbed soil)with shaker (undisturbed soil)after forced vibration test (mass = 0.65 kg))after forced vibration test (mass = 2.65 kg)after forced vibration (w/o shaker)

N

Shaking Direction

Figure 5.8 Frequency Response Functions for 1.2-m CIDH Pile (No.1) from Impact Vibration Tests (E-W Direction)

163

0 10 20 30 40 50Frequency (Hz)

0

0.1

0.2

0.3

Am

plitu

de (g

/N)

without shaker (undisturbed soil)with shaker (undisturbed soil)after forced vibration test (mass = 0.65 kg)after forced vibration test (mass = 2.65 kg)

N

Shaking Direction

Figure 5.9 Frequency Response Functions for 1.2-m CIDH Pile (No.2) from Impact Vibration Tests (E-W Direction)

0 10 20 30 40 50Frequency (Hz)

0.001

0.01

0.1

1

10

Am

plitu

de (g

/N)

0.4-m0.6-m0.9-m+mass1.2-m (No.1)1.2-m (No.2)

Figure 5.10 Comparison of Frequency Response Functions for Various Pile Diameters from Impact Vibration Tests (E-W Direction)

164

6 8 10 12 14Frequency (Hz)

0

0.02

0.04

0.06

0.08

0.1

Nor

mal

ized

Acc

eler

atio

n, a

/ω2 (

mg-

s2 )

m = 0.65 kg (Test 1)m = 0.65 kg (Test 2)m = 0.65 kg (Test 3)m = 0.65 kg (Test 4)m = 0.65 kg (Test 5)

N

Shaking Direction


6 8 10 12 14 16 18 20Frequency (Hz)

0

0.04

0.08

0.12

0.16

0.2

Nor

mal

ized

Acc

eler

atio

n, a

/ω2 (m

g-s2 )

m = 0.65 kg (Test 1)m = 0.65 kg (Test 2)m = 0.65 kg (Test 3)m = 1.46 kg (Test 1)m = 1.46 kg (Test 2)m = 1.46 kg (Test 3)m = 2.06 kg (Test 1)m = 2.06 kg (Test 2)m = 2.06 kg (Test 3)

N

Shaking Direction


165

6 8 10 12 14 16 18 20Frequency (Hz)

0

0.04

0.08

0.12

0.16

0.2

Nor

mal

ized

Acc

eler

atio

n, a

/ω2 (m

g-s2 )

m = 2.06 kg (Test 3)m = 0.65 kg (Test 14)m = 1.46 kg (Test 7)m = 2.06 kg (Test 6)

N

Shaking Direction

Figure 5.13 Frequency Response Curves for 0.6-m Pile from Forced Vibration Tests (after Pile Experienced Highest Amplitude of Excitation Force)

8 10 12 14 16 18 20 22 24 26 28Frequency (Hz)

0

0.02

0.04

0.06

0.08

0.1

0.12

Nor

mal

ized

Acc

eler

atio

n, a

/ω2 (m

g-s2 )

m = 1.46 kg (Test 1)m = 1.46 kg (Test 2)m = 1.46 kg (Test 3)m = 2.65 kg (Test 1)m = 2.65 kg (Test 2)

N

Shaking Direction


166

8 10 12 14 16 18 20 22 24 26 28Frequency (Hz)

0

0.02

0.04

0.06

0.08

0.1

0.12

Nor

mal

ized

Acc

eler

atio

n, a

/ω2 (

mg-

s2 )


N

Shaking Direction

after lateral load test

Figure 5.15 Frequency Response Curves for 0.9-m Pile from Forced Vibration Tests (after Pile Experienced Highest Amplitude of Excitation Force)

10 15 20 25 30 35 40Frequency (Hz)

0

0.01

0.02

0.03

0.04

0.05

0.06

Nor

mal

ized

Acc

eler

atio

n, a

/ω2 (m

g-s2 )

m = 0.65 kg (Test 1)m = 0.65 kg (Test 2)m = 0.65 kg (Test 3)m = 1.46 kg (Test 1)m = 1.46 kg (Test 2)m = 1.46 kg (Test 3)m = 2.06 kg (Test 1)m = 2.06 kg (Test 2)m = 2.06 kg (Test 3)m = 2.65 kg (Test 1)m = 2.65 kg (Test 2)m = 2.65 kg (Test 3)

N

Shaking Direction

Figure 5.16 Frequency Response Curves for 1.2-m Pile (No.1) from Forced Vibration Tests

167

10 15 20 25 30 35 40Frequency (Hz)

0

0.01

0.02

0.03

0.04

0.05

0.06

Nor

mal

ized

Acc

eler

atio

n, a

/ω2 (

mg-

s2 )


N

Shaking Direction

Figure 5.17 Frequency Response Curves for 1.2-m Pile (No.1) from Forced Vibration Tests (after Pile Experienced Highest Amplitude of Excitation Force)

10 15 20 25 30 35 40 45Frequency (Hz)

0

0.01

0.02

0.03

Nor

mal

ized

Acc

eler

atio

n, a

/ω2 (m

g-s2 )

m = 0.65 kg (Test 1)m = 0.65 kg (Test 2)m = 0.65 kg (Test 3)m = 1.46 kg (Test 1)m = 1.46 kg (Test 2)m = 1.46 kg (Test 3)m = 2.06 kg (Test 1)m = 2.06 kg (Test 2)m = 2.06 kg (Test 3)m = 2.65 kg (Test 1)m = 2.65 kg (Test 2)m = 2.65 kg (Test 3)

N

Shaking Direction

Figure 5.18 Frequency Response Curves for 1.2-m Pile (No.2) from Forced Vibration Tests

168

10 15 20 25 30 35 40 45Frequency (Hz)

0

0.01

0.02

0.03

Nor

mal

ized

Acc

eler

atio

n, a

/ω2 (

mg-

s2 )


N

Shaking Direction

Figure 5.19 Frequency Response Curves for 1.2-m Pile (No.2) from Forced Vibration Tests (after Pile Experienced Highest Amplitude of Excitation Force)

0 10 20 30 40Frequency (Hz)

0

0.1

0.2

0.3

0.4

0.5

0.6

Nor

mal

ized

Acc

eler

atio

n, a

/mω

2 r (m

g/N

)

0.4-m0.6-m0.9-m1.2-m (No.1)1.2-m (No.2)

Figure 5.20 Comparison of Frequency Response Curves for Various Pile Diameters from Forced Vibration Tests

169

-0.04

-0.02

0

0.02

0.04

Acc

eler

atio

n (g

) a) 0.4-m Pile

-0.04

-0.02

0

0.02

0.04

Acc

eler

atio

n (g

) b) 0.6-m Pile

-0.04

-0.02

0

0.02

0.04

Acc

eler

atio

n (g

) c) 0.9-m Pile

0 0.5 1 1.5Time (s)

-0.04

-0.02

0

0.02

0.04

Acc

eler

atio

n (g

) d) 1.2-m Pile (Pile No.1)

Figure 5.21 Acceleration vs. Time for CIDH Piles from Impact Vibration Tests (E-W Direction)

170

0 0.5 1 1.5Diameter (m)

0

10

20

30

Dam

ping

Rat

io (%

)Forced Vibration TestImpact Vibration Test

Figure 5.22 Comparison of Damping Ratio Obtained from Impact and Forced Vibration Tests

0 0.5 1 1.5 2 2.5 3Mass of Bucket (kg)

0

10

20

30

Dam

ping

Rat

io (%

)

0.4-m Pile0.6-m Pile0.9-m Pile1.2-m Pile

Figure 5.23 Relationship between Mass of Bucket and Damping Ratio for Various Pile Diameters

171

6

4

2

0

-2D

epth

(m)

0 0.4 0.8 1.2Normalized Amplitude

0.4-m (Acc.)0.4-m (S.G.)0.6-m (S.G.)0.9-m (S.G.)1.2-m No.1 (Acc.)1.2-m No.2 (Acc.)

Acc. = Used Data from AccelerometersS.G. = Used Data from Strain Gauges

Figure 5.24 Mode Shape of Each Pile

172

0 20 40 60 80 100Displacement (mm)

0

200

400

600

Load

(kN

)

0.9-m Pile (Phase I)

0.6-m Pile0.9-m Pile (Phase II)

Figure 5.25 Static Load-Displacement Curves for 0.6-m and 0.9-m CIDH Piles before Correction


0

200

400

600

Load

(kN

)

From Phase I

From Phase II

From Phase I (x0.75 on Load)

Figure 5.26 Static Load-Displacement Curves of 0.9-m Pile Obtained from Phase I and Phase II

173


0

100

200

300

400

500

Load

(kN

)

0.9-m Pile

0.6-m Pile

Figure 5.27 Static Load-Displacement Curves for 0.6-m and 0.9-m CIDH Piles after Correction

-400 -200 0 200 400Displacement (mm)

-600

-400

-200

0

200

400

600

Load

(kN

)

Push

Pull

Static

1.9 2.6 3.8 5.0 6.4 7.48.1µ∆

Figure 5.28 Cyclic Load-Displacement Curve for 0.6-m CIDH Pile after Correction

174

-4000 0 4000 8000 12000Longitudinal Strain (x10-6)

12

10

8

6

4

2

0

-2

Dep

th (m

)

30 kN94 kN150 kN257 kN340 kN384 kN

comp. tens.

A-DirectionP

B-Direction

1.09 m

A

B

C

D

P

-4000 0 4000 8000 12000Longitudinal Strain (x10-6)

12

10

8

6

4

2

0

-2

Dep

th (m

)

comp. tens.

Applied Load

-4000 -2000 0 2000 4000Longitudinal Strain (x10-6)

12

10

8

6

4

2

0

-2

Dep

th (m

)

30 kN94 kN150 kN257 kN340 kN384 kN

comp. tens.

C-Direction D-Direction

A

B

C

D

P


12

10

8

6

4

2

0

-2

Dep

th (m

)

comp. tens.

Applied Load

1.09 m


175

-500 -250 0 250 500Spiral Strain (x10-6)

3

2

1

0D

epth

(m)

94 kN150 kN257 kN340 kN384 kN404 kN

-500 -250 0 250 500Spiral Strain (x10-6)

3

2

1

0

Dep

th (m

)

-500 -250 0 250 500Spiral Strain (x10-6)

3

2

1

0

Dep

th (m

)

-500 -250 0 250 500Spiral Strain (x10-6)

3

2

1

0

Dep

th (m

)

comp. ten.

A Direction B Direction

C Direction D Direction

comp. ten.

comp. comp. ten.ten.

Figure 5.30 Strain Distribution in Transverse Reinforcement for 0.6-m CIDH Pile

176

Figure 5.31 Rupture of Spiral Reinforcement and 3 Longitudinal Bars in A Direction

Figure 5.32 Rupture of 2 Longitudinal Bars in C Direction

177

Figure 5.33 Severe Damage of 0.6-m CIDH Pile between Depths 0 m and 0.6 m

Figure 5.34 Crack Patterns along 0.6-m CIDH Pile

178

0 50 100 150Displacement (mm)

0

400

800

1200

1600

Load

(kN

)

0.9-m Pile1.2-m Pile

Figure 5.35 Static Load Displacement Curves for 0.9-m and 1.2-m CIDH Piles

-600 -400 -200 0 200 400 600Displacement (mm)

-2000

-1500

-1000

-500

0

500

1000

1500

2000

Load

(kN

)

Push

Pull

Static

2.22.8

3.4 4.5 5.6 7.6 8.71.7µ∆

Figure 5.36 Cyclic Load-Displacement Curve for 0.9-m CIDH Pile

179


12

10

8

6

4

2

0

-2

Dep

th (m

)

214 kN423 kN636 kN845 kN1059 kN

comp. tens.

A-DirectionP

B-Direction

1.10 m

A

B

C

DP


12

10

8

6

4

2

0

-2

Dep

th (m

)

comp. tens.

Applied Load


12

10

8

6

4

2

0

-2

Dep

th (m

)

214 kN423 kN636 kN845 kN1059 kN

comp. tens.

C-DirectionP

D-Direction

1.10 m

A

B

C

DP


12

10

8

6

4

2

0

-2

Dep

th (m

)

comp. tens.

Applied Load


180

Figu

re 5

.38

Cra

ck P

atte

rns a

long

0.9

-m C

IDH

Pile

at D

epth

s bet

wee

n (a

) 0 m

and

1.2

m, a

nd (b

) 0.9

m a

nd 2

.4 m

181

0 10 20 30 40Displacement (mm)

0

40

80

120

160

Load

(kN

)

Figure 5.39 Static Load Displacement Curve for 0.4-m CIDH Piles

-300 -200 -100 0 100 200 300Displacement (mm)

-300

-200

-100

0

100

200

300

Load

(kN

)

Push

Pull

Static1.7 2.32.9 3.5 4.6 5.8 6.9µ∆

Figure 5.40 Cyclic Load-Displacement Curve for 0.4-m CIDH Pile

182


5

4

3

2

1

0

-1

-2

Dep

th (m

)

20 kN40 kN60 kN80 kN100 kN120 kN139 kN

comp. tens.

A-Direction

P

B-Direction

0.66 m

P


5

4

3

2

1

0

-1

-2

Dep

th (m

)

Applied Load

comp. tens.

A

B C

D


5

4

3

2

1

0

-1

-2

Dep

th (m

)

20 kN40 kN60 kN80 kN100 kN120 kN139 kN

comp. tens.

C-Direction D-Direction

P


5

4

3

2

1

0

-1

-2

Dep

th (m

)

comp. tens.

A

B C

D

P

0.66 m

Applied Load


183

Figure 5.42 Rupture of Reinforcing Steels of 0.4-m CIDH Pile at Depth of 0.3 m

Figure 5.43 Crack Patterns along 0.4-m CIDH Pile at Depths between 0 m and 1.2 m

184

0 50 100 150Displacement (mm)

0

500

1000

1500

2000

2500

Load

(kN

)

Pile No.2Pile No.1

Figure 5.44 Static Load Displacement Curves for 1.2-m CIDH Piles

-600 -400 -200 0 200 400 600Displacement (mm)

-3000

-2000

-1000

0

1000

2000

3000

Load

(kN

)

Push

Pull

Pile No.2

Pile No.1 2.1 4.1 5.2 6.2µ∆

Figure 5.45 Cyclic Load-Displacement Curves for 1.2-m CIDH Piles

185


12

10

8

6

4

2

0

-2

Dep

th (m

)

285 kN574 kN858 kN1148 kN1432 kN1717 kN1948 kN

comp. tens.

A-DirectionP

B-Direction

0.83 m

A

BC

DP


12

10

8

6

4

2

0

-2

Dep

th (m

)

comp. tens.

Applied Load


12

10

8

6

4

2

0

-2

Dep

th (m

)

285 kN574 kN858 kN1148 kN1432 kN1717 kN1948 kN

comp. tens.

C-DirectionP

D-Direction

0.83 m

A

BC

DP


12

10

8

6

4

2

0

-2

Dep

th (m

)

comp. tens.

Applied Load

Figure 5.46 Strain Distribution in Longitudinal Reinforcement for 1.2-m CIDH Pile (No.1)

186


12

10

8

6

4

2

0

-2

Dep

th (m

)

285 kN574 kN858 kN1148 kN1432 kN1717 kN1948 kN

comp. tens.

A-DirectionP

B-Direction

0.95 m

A

BC

DP


12

10

8

6

4

2

0

-2

Dep

th (m

)

comp. tens.

Applied Load


12

10

8

6

4

2

0

-2

Dep

th (m

)

285 kN574 kN858 kN1148 kN1432 kN1717 kN1948 kN

comp. tens.

C-DirectionP

D-Direction

0.95 m

A

BC

DP


12

10

8

6

4

2

0

-2

Dep

th (m

)

comp. tens.

Applied Load

Figure 5.47 Strain Distribution in Longitudinal Reinforcement for 1.2-m CIDH Pile (No.2)

187

Figu

re 5

.48

Cra

ck P

atte

rns a

long

1.2

-m P

ile (

No.

2) a

t Dep

ths b

etw

een

(a) 0

.75

m a

nd 1

.5 m

, and

(b) 1

.5 m

and

4.5

m

188

-0.4 0 0.4 0.8 1.2

Normalized Strain

12

10

8

6

4

2

0

-2

Rat

io o

f Dep

th to

Pile

Dia

met

er, z

/D


Mmax~1.0 to 3.0 D

M0~6.0D

Figure 5.49 Normalized Strain vs. Ratio of Depth to Pile Diameter

189

-400

-200

020

040

0D

ispl

acem

ent (

mm

)

-600

-400

-2000

200

400

600

Load (kN)

Pus

h

Pull

Stat

ic

1.9

2.6

3.8

5.0

6.4

7.4

8.1

µ ∆(b

)

-600

-400

-200

020

040

060

0D

ispl

acem

ent (

mm

)

-300

0

-200

0

-100

00

1000

2000

3000

Load (kN)

Pus

h

Pull

Pile

No.

2

Pile

No.

12.

14.

15.

26.

2µ ∆

(d)

-300

-200

-100

010

020

030

0D

ispl

acem

ent (

mm

)

-300

-200

-1000

100

200

300

Load (kN)P

ush

Pul

l

Sta

tic1.

72.

32.9

3.5

4.6

5.8

6.9

µ ∆(a

)

-600

-400

-200

020

040

060

0D

ispl

acem

ent (

mm

)

-200

0

-150

0

-100

0

-5000

500

1000

1500

2000

Load (kN)

Push

Pul

l

Sta

tic

2.22.

8 3.4

4.5

5.6

7.6

8.7

1.7

µ ∆(c

)

Figu

re 5

.50

Cyc

lic L

oad-

Dis

plac

emen

t Cur

ves f

or a

) 0.4

-m P

ile, b

) 0.6

-m P

ile, c

) 0.9

-m P

ile, a

nd (d

) 1.2

-m P

iles

190


191

Chapter 6 ANALYSIS OF TEST RESULTS

In this chapter, the evaluation of the effect of pile diameter on modulus of

subgrade reaction using the results from full-scale experiments is presented. The effect

of the pile diameter on the initial modulus of subgrade reaction, the initial slope of p-y

curves, was evaluated using the results from impact vibration tests. This is followed by

the evaluation of the effect of pile diameter on p-y curves at larger strain levels using the

back-calculated p-y curves based on the results from lateral load testing. Furthermore,

based on the back-calculated p-y curves, the methodology to construct the p-y curves for

the weakly cemented soil was proposed and validated with the results from full-scale

lateral load testing.

6.1 Pile Diameter Effect on Initial Modulus of Subgrade Reaction

In this section, the natural frequencies of soil-pile systems based on the results of

the impact vibration tests were used to evaluate the pile diameter effect on the initial

modulus of subgrade reaction at a very small strain level. The measured natural

frequencies were compared with those estimated from a numerical model. The soil

springs in the numerical model were established by implementing three different

concepts on initial modulus of subgrade reaction. One is based on Terzaghi’s concept

(Terzaghi 1955) in which the modulus of subgrade reaction is independent of pile

diameter. Another was based on recent research by Carter (1984) and Ling (1988)

suggesting that the initial modulus of subgrade reaction may be linearly proportional to

pile diameter. The last one was developed based on the findings from finite element

analyses in Chapter 3, in which the pile diameter had a little effect on the modulus of

subgrade reaction.

192

6.1.1 Method of Analysis

In order to verify the influence of pile diameter on initial modulus of subgrade

reaction, a numerical model of the soil-pile system was developed as presented in Figure

6.1. The pile was modeled by using a series of beam elements. The mass distributed

throughout the pile element was idealized as a concentrated mass at the nodal points. The

flexural rigidity of the pile, EpIp, was computed based upon the uncracked concrete

section. Though minor cracking due to shrinkage may be present, these will have an

insignificant effect on the stiffness of the pile (Hsu 1993). A summary of flexural rigidity

of each pile is presented in Table 6.1. Soil around the pile was modeled by using a series

of linear Winkler springs evenly spaced at 0.15 m along the pile length. Since the

stepped soil profile is common in weakly cemented sands (e.g. Ashford and Sitar 1994), a

simple two-layer soil system seemed to be reasonable to represent the site condition.

However, an alternative soil profile with its stiffness increasing with depth was also

considered in this analysis. A polynomial function was used to fit the travel time data,

and then the shear wave velocity based on this function was computed. The travel-time

curve together with associated shear wave velocity for both possible types of soil profiles

are presented in Figure 6.2.

Three types of soil springs were considered in this study. One was developed

based on Terzaghi’s (1955) conclusion in which the modulus of subgrade reaction is

independent of pile diameter (i.e., Kind). Another one was developed based on Carter

(1984) and Ling’s (1988) conclusions in which the modulus of subgrade reaction is

linearly dependent on pile diameter (i.e., Kdep). The last one was developed based on the

finding obtained from the finite element analysis (i.e., Kfin) in Chapter 3 in which the pile

diameter has a small effect on the initial modulus of subgrade reaction (i.e. 364.0

2

1

2

1⎟⎟⎠

⎞⎜⎜⎝

⎛=

DD

KK or refer to Eq. (3.3) in Chapter 3).

193

The Vesic’s equation (Eq. 2.3) is usually used to estimate the modulus of

subgrade reaction from the soil’s Young’s modulus for the linear elastic range. The soil

spring stiffness can therefore be estimated from the shear wave velocity and the equation

modified from the Vesic’s Equation, Eq. (2.3) (Ling 1988). The solution obtained from

Eq. (2.3) is taken from the beam on the elastic foundation case. Bowles (1988) suggested

a modification on Eq. (2.3) in that the modulus of subgrade reaction, K, for the lateral

loaded pile case should be doubled since the pile has soil contact with both sides.

However, in reality, soil does not have contact all around the pile when the pile is

subjected to lateral loading, but the friction developed at both sides of the pile can

increase the overall soil resistance. The average value from lower bound, Eq. (2.3), and

upper bound solutions suggested by Bowles seems to be reasonable for the analysis of the

laterally loaded pile. This is in agreement with what was proposed by Carter (1984) and

Ling (1988) who found that the closest agreement in predicting the pile deflection was

obtained by using a factor of 1.0 as

12/1

4

2 )1(0.1

⎥⎥⎦

⎤

⎢⎢⎣

⎡

−=

pp

s

s

s

IEDEE

Kµ

(6.1)

To account for the effect of pile diameter on initial modulus of subgrade reaction,

Carter and Ling suggested a linear relationship between the modulus of subgrade reaction

and the pile diameter, K, based on Ling’s concept can then be expressed as

12/1

4

2 )1(0.1

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

−=

pp

s

refs

s

IEDE

DDE

Kµ

(6.2)

where Dref = 1.0 m.

Similar to Eq. (6.2), the modulus of subgrade reaction which incorporated the pile

diameter effect based on the finding from the finite element analysis in Chapter 3 can be

calculated as follows:

194

12/14

364.0

2 )1(0.1

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

−=

pp

s

refs

s

IEDE

DDE

Kµ

(6.3)

The soil elastic modulus, Es, can be determined by

)1(2 2sss VE µρ += (6.4)

where ρ = soil density, and Vs = shear wave velocity.

From the above expressions, the initial horizontal modulus of subgrade reaction

can be calculated. Kind, Kdep, and Kfin can be determined by using Eq. (6.1),

(6.2) and (6.3), respectively. The soil spring stiffness can then be computed by

multiplying the modulus of subgrade reaction with the soil spring spacing. A summary

of soil spring stiffnesses based on different concepts of pile diameter effect on modulus

of subgrade reaction for simple two-layer soil system is given in Table 6.1.

Based on the numerical model of soil-pile system, the mass matrix [ ]M and

stiffness matrix [ ]K can be simply formulated. The mode shape and natural frequency of

the system can then be calculated by using a modal analysis. Taking the equation of

undamped free vibration, where no loads are assumed to act upon the structure, the N

degree-of –freedom equation of equilibrium becomes

[ ] [ ]{ } { }0..

=+⎭⎬⎫

⎩⎨⎧ uKuM (6.5)

where { }u and ⎭⎬⎫

⎩⎨⎧ ..

u are the displacement and acceleration vector of an multi-degree-of-

freedom system. By assuming simple harmonic motion { } { } tYu iii ωsinΦ= the equation

of free vibration is then simplified to

195

[ ]{ } [ ]{ } { }02 =Φ+Φ− iii KMω (6.6)

where { }iΦ , iω , and Yi are the ith mode, frequency, and modal amplitude of free vibration

respectively.

The damped natural frequency of the system was then calculated as

21 ξωω −= nD (6.7)

where Dω = damped natural frequency, nω = undamped natural frequency (from Eq. 6.6),

and ξ = damping ratio of the system (obtained from impact vibration test results).

In this study, the Ruaumoko program (Carr 1998), a structural analysis program

for inelastic dynamic analysis, was utilized to run a modal analysis to predict the natural

frequency of the soil-pile system.

6.1.2 Results of Analyses

The computed natural frequencies based on the different concepts on initial

modulus of subgrade reaction for a case of simple 2-layer soil profile are given in Table

6.2. It is noted that for the 1.2-m piles, the computed natural frequency of Pile No.1 is

higher than that of Pile No.2 because the free standing height of Pile No.1 was lower than

that of Pile No.2. The comparison between experimental and computational results was

made by plotting the ratio of computed to measured natural frequency against the pile

diameter as shown in Figure 6.3 through Figure 6.6. From Figure 6.3, it is clearly seen

that for the simple two-layer soil profile the results obtained from Terzaghi’s concept

(i.e., Kind) give a good agreement on natural frequency prediction over the range of the

diameter considered. The computed natural frequency of the system based on Kdep

appears to be significantly underestimated at diameters less than 1 m and slightly

196

overestimated beyond that diameter. Since Terzaghi’s approach is consistent with the

test results, the comparison between the two concepts can be extrapolated over a wider

range of pile diameters by performing a parametric study. The results are shown by the

dotted line in Figure 6.3, which confirms the trends above and below the 1-m diameter.

Figure 6.4 shows that the soil springs developed from both Terzaghi’s concept and the

conclusion from the finite element analysis gave reasonable agreement between the

computed and the measured natural frequency with similar degree of accuracy. From

this, it is inferred that the initial modulus of subgrade reaction for weakly cemented sand

appears to have insignificant effect on the pile diameter.

In contrast to Figure 6.4, Figure 6.5 presents the ratio of computed to measured

natural frequency against pile diameter using a soil profile where the soil stiffness

increases with depth. Though the computed natural frequencies derived from Terzaghi’s

concept and finite element analysis finding are in better agreement with the measured

natural frequency than those obtained from Ling’s concept, all of them underestimated

the natural frequency with the difference being more significant at a small pile diameter.

Additional analyses were conducted to see whether or not the trend of the pile diameter

effect will change, if the spring stiffnesses at all depths were increased. Assuming that

the equations used to calculate the spring stiffnesses were conservative, the spring

stiffnesses were therefore calibrated by multiplying them with a constant until the

computed natural frequency of the 1.2-m pile matched well with the measured natural

frequency. Analyses were then performed for other diameters using the updated spring

stiffnesses. The improvement on the natural frequency prediction was observed as

presented in Figure 6.6, but there was no change in the trend. This implies that the

simple two-layer soil profile seems to be more appropriate to represent the behavior of

cemented soil at a very small strain level. Unlike clean sand whose stiffness increases

with depth due to the effect of confining pressure, the behavior of cemented sand at very

small strain seems to be independent of depth. This is because at very small strain level

the cohesion is the predominant strength component, and therefore the confinement of the

197

soil does not have much effect on its initial stiffness (Saxena and Lastrico 1978). This

finding was also supported by previous research on behavior of artificially cemented sand

(Clough et al. 1981) presented in Figure 2.25d in Chapter 2, which indicates that the

initial modulus of the artificially cemented soil at small strain is independent on the

confining pressure.

6.1.3 Analysis of Damping

In this section the damping ratio of the systems were estimated using the available

equations in the literature to compare with the damping ratio measured from the impact

vibration experiments. Gazetas (1991) proposed closed-form expressions to estimate the

static stiffnesses and damping coefficients (i.e., KHH, KMM, KHM, ξHH, ξMM, and ξHM) for

flexible piles in constant stiffness soil profile as the followings:

21.0)/( spsHH EEDEK = (6.8)

75.03 )/(15.0 spsMM EEEDK = (6.9)

50.02 )/(22.0 spsMHHM EEEDKK −== (6.10)

sspHH VEEfD /)/(10.180.0 17.0+≈ βξ (6.11)

sspMM VEEfD /)/(35.035.0 20.0+≈ βξ (6.12)

sspHM VEEfD /)/(85.085.0 18.0+≈ βξ (6.13)

where KHH, KMM, and KHM are static lateral, static rocking, and static swaying-rocking

cross stiffnesses of the pile, ξHH, ξMM, and ξHM are lateral, rocking, and swaying-rocking

damping coefficients, D is pile diameter, β is material damping ratio of the soil, Vs is

shear wave velocity, f is frequency excitation, Ep is the Young’s Modulus of pile, and Es

is the Young’s modulus of the soil.

198

The horizontal static stiffness, Kh, and rotational static stiffness, Kθ, of the pile can

be estimated by using the following equations:

HMKKKKKΚ

HMMM

HMMMHHh −

−=

2

(6.14)

MHKK

KKKKHMHH

HMMMHH

−−

=2

θ (6.15)

where H is the horizontal force at the pile head, and M is the moment at the pile head.

The various components of the pile head impedances, σαβ, can be determined as

)2( ikK αβαβαβαβ ξσ += (6.16)

where αβ refers to various components (i.e., HH, MM, and HM), Kαβ is the static pile

head stiffness (from Eqs. (6.8) through (6.10)), kαβ is the dynamic stiffness coefficient,

which is approximately equal to one (Gazetas 1991), and ξαβ is the damping coefficients

(from Eqs. (6.11) through (6.13)).

The horizontal and rotational pile head impedances (i.e., σh and σθ) can be

determined in the same fashion as Eqs. (6.14) and (6.15) by replacing Kαβ terms with σαβ

terms as:

HMHMMM

HMMMHHh /

2

σσσσσ

σ−

−= (6.17)

MHHMHH

HMMMHH

/

2

σσσσσ

σ θ −−

= (6.18)

199

The σh and σθ are in complex form similar to Eq. (6.16). The horizontal and

rotational dampings (ξh and ξθ) can then be simply calculated as the ratio between the

imaginary part and two times of the real part. Wolf (1985) proposed the equation to

estimate the equivalent damping of SDOF system with the pile foundation as

θ

θθξξξ

ξ

Khk

Kk

Khk

Kk

st

h

st

st

h

sthst

2

2

1 ++

++= (6.19)

where: stξ is the damping for the structure, stk is the stiffness of the structure, and h is

the height of the SDOF structure.

The damping ratio of each pile was calculated using the above expressions and

then compared with the measured one as presented in Figure 6.7. The results show a

good agreement between predicted and measured damping, though they were somewhat

higher than those computed, particularly at high frequencies. This might be due to two

possible reasons: (1) the analytical solutions used in this analysis were derived based

upon single constant soil modulus, while the soil at the test site consisted of two constant

soil modulus layers system, and (2) the damping ratio determined based on logarithmic

decrement method at high frequency might have some error due to the limited number of

acceleration amplitude peaks during the free vibration testing. The computed damping

ratios based on analytical solutions were lower than the measured damping ratios

indicating that Gazetas’s damping expressions are conservative for the soil and piles

tested.

6.2 Pile Diameter Effect on p-y Curves

In the previous section, it was shown that the pile diameter has an insignificant

effect on the initial modulus of subgrade reaction, the initial stiffness of p-y curve. In this

200

section, the back-calculated p-y curves based on the results from static lateral load tests

for various pile diameters are presented. The p-y curves of each pile at different depths

were then compared to provide insight into the effect of pile diameter on p-y curves at

larger strain level.

6.2.1 Method for Back-Calculating p-y Curves

The lateral soil resistance per unit pile length developed along the CIDH piles, p,

as well as associated soil-pile displacement, y, were back-calculated using the basic beam

theory. The strain gauge data was utilized extensively in the back-computation of the p-y

curves. Only data from the static tests was used in the analyses because the strain gauge

data during the cyclic loading was inconsistent due to the yielding of the pile. The

methodology used to calculate p-y curves is described as the following:

To determine the lateral soil resistances as well as associated pile displacements,

the curvature of the pile, φ, at each depth was first determined using the strain gauge data.

For a steel pipe pile, the neutral axis of the pile remains at the center throughout the test

and data from two strain gauges per depth seems to be sufficient to calculate the

curvature. In contrast, estimation of the curvature in the reinforced concrete pile is more

difficult because the strain measured along the pile is not uniform. The strain is high in

the vicinity of the crack and lower at a location far away from the crack. Therefore, more

strain gauges are required at each depth in order to obtain reliable curvature. In this study

three to four strain gauges were available at each depth. Figure 6.8 presents an example

of curvature estimation based on good strain gauge data. Assuming a linear distribution

of strain along the pile cross section, the curvature of the pile can be determined using the

best fit of a linear function to the strain gauge data. The slope of the linear function

represents the curvature of the pile.

201

The 6th order polynomial function was chosen to fit the discrete curvature. Then

the rotation of the pile, θ, was computed by an integration of the curvature polynomial

function along the pile length using the following equation:

∫= dzz)(φθ (6.20)

where: θ is pile rotation, φ(z) is polynomial curvature function, and z is depth.

At this step, the computed rotation along the pile was compared to the measured

rotation from the tiltmeters to confirm that the fit polynomial function was reasonable.

Subsequently, the soil displacements, y, were determined by integrating the polynomial

function of pile rotation along the pile length using the following expression:

∫= dzzy )(θ (6.21)

In order to determine the soil resistance along the pile, the moment of the pile was

first computed using the following expression:

φ*EIM = (6.22)

where M is the moment, EI is flexural rigidity or flexural stiffness of the pile, and φ is the

pile curvature. Since the EI of CIDH pile is not constant, the UCFyber (Chadwell 1999),

a finite element program for section analysis, was used to obtain the moment-curvature

relationship for each pile. Figure 6.9 through Figure 6.12 present the moment-curvature

relationship for each pile together with the simplified ones using a quadruple-linear

model for the analyses. It is noted that beyond the yield moment, the analyses were not

conducted due to the inconsistency of strain gauge data. However the simplified

moment-curvature relationship for the entire curves is used for a prediction of load–

202

displacement curves in the inelastic range of the piles, which will be discussed in the

subsequent section.

Again, the 6th order polynomial function was chosen to fit the discrete moment

data along the length of the pile. The shear forces along the length of the pile were

calculated by differentiating the moment data with respect to depth using the following

relationship:

dzzdMS )(

= (6.23)

where S is shear force, M is moment and z is depth.

At this step, the calculated shear force at ground surface was compared with the

measured shear force from the actuator load. This step was to confirm that the

polynomial function chosen to fit the moment data was reasonable. Then, the lateral soil

resistance was determined by the following equation:

dzzdSp )(

= (6.24)

where p is the soil resistance per unit pile length , z is depth, and S is shear force. With

the lateral soil resistance and associated pile displacement computed from the above

equations, the p-y curves of the soil at each depth can be obtained.

203

6.2.2 Back-Calculated p-y Curves for CIDH Piles

6.2.2.1 0.4-m p-y Curves

Figure 6.13 shows the back-calculated p-y curves of the 0.4-m CIDH pile at

various depths based on the methodology mentioned in previous section. It can be

observed that the soil resistance increases with depth. Furthermore, the soil resistance at

the ground surface is not zero as usually assumed in the sand p-y curves (Reese et al.

1974). This is likely because the soil at the test site was weakly cemented sand, and that

the cementation, in the form of cohesion, contributed to the soil resistance at the ground

surface. The characteristic shape of the back-calculated p-y curves is similar to that

proposed by Ismael (1990) rather than that proposed by Reese and Van Impe (2001) in

which the softening of the p-y curves is expected.

Since the double differentiation of the moment along the pile may lead to a

significant error in estimating the soil resistance, a verification of the p-y curves was

required at the end of the process. The back-calculated p-y curves were used as the input

in a numerical model (i.e., beam with a series of nonlinear springs) to predict the lateral

responses of the piles and then to compare with the experimental results. Good

agreement between computed and measured responses was observed as presented in

Figure 6.14 and Figure 6.15, indicating that that the back-calculated p-y curves for the

0.4-m pile are reasonable.

6.2.2.2 0.6-m p-y Curves

Figure 6.16 shows the back-calculated p-y curves of the 0.6-m CIDH pile at

various depths. Similar characteristics of the p-y curves as observed in the 0.4-m pile

were also seen in the 0.6-m pile. After the p-y curves were back-calculated, the analysis

was performed to verify that the back-calculated p-y curves provide a reasonable estimate

204

of the pile response. Figure 6.17 and Figure 6.18 show the pile responses from the

analysis compared to measured test results.

6.2.2.3 0.9-m p-y Curves

The back-calculated p-y curves of the 0.9-m CIDH pile using the strain gauge data

from lateral load test No.2 is presented in Figure 6.19. The results indicate that the soil

resistance increases with depth and there is a finite soil resistance observed at the ground

surface. Figure 6.20 and Figure 6.21 show the results of the analysis using back-

calculated p-y curves compared to the measured test results. Good agreement between

measured and computed responses are observed showing that these back-calculated p-y

curves can reproduce the good estimate of the pile response.

6.2.2.4 1.2-m p-y Curves

The back-calculated p-y curves of the 1.2-m CIDH pile (No.1) are presented in

Figure 6.22. The first portions of p-y curves (i.e., up to the lateral load of 845 kN) were

back-calculated based on the results from lateral load test No.2 while the remaining parts

(i.e, from 1059 kN to 1948 kN) were obtained from the results of lateral load test No.4.

The reason for not using the data of the lateral load test No.4 to back-calculate the entire

p-y curves is that gapping surrounding pile No.1 was observed before test No.4. This

gapping developed during lateral load test No.2 when pile No.1 was served as a reaction

to test the 0.9-m pile. Using only the results from lateral load test No.4 would drastically

underestimate the soil resistance. The characteristic of the p-y curves for the 1.2-m pile

(No.1) were similar as those observed in the previous other piles. After p-y curves were

back-calculated, an analysis was performed to verify the accuracy of the p-y curves in

predicting the pile response. A comparison between the measured and computed

responses using the back-calculated p-y curves are shown in Figure 6.23 and Figure 6.24,

verifying that the back-calculated p-y curves are reasonable.

205

Figure 6.25 presents the p-y curves of the 1.2-m pile (No.2) back-calculated from

the results of lateral load test No.4. Excellent agreement between measured and

computed responses was observed as presented in Figure 6.26 and Figure 6.27 indicating

that these back-calculated p-y curves provided the decent estimate of the pile response.

6.2.3 Comparison of p-y Curves for Different Pile Diameters

A comparison of the p-y curves from the results of full-scale lateral load tests on

various pile diameters provides insight into the effect of pile diameter on the p-y curves.

Figure 6.28 presents a comparison of the p-y curves of all pile diameters at different

depths. It is observed that the back-calculated p-y curves for all piles are generally

similar indicating that the pile diameter has insignificant effect on p-y curves. The p-y

curves of the 1.2-m (No.2) are in good agreement with those of the 1.2-m (No.1) up to

the displacement of approximately 10 mm. Beyond that the p-y curves of Pile No.1 are

stiffer than those of Pile No.2. This is likely because Pile No.2 was located close to the

natural slope, and therefore the soil confining pressure which affected the soil resistance

at large strain level was less than that of Pile No.1 causing the lower soil resistance.

Similarity of back-calculated p-y curves for different pile diameters indicates that

the pile diameter seems to have an insignificant effect on the p-y curves for the

displacement range of testing. This can be explained by considering the p-y curves at

depth below 0.6 m. The characteristics of back-calculated p-y curves were somewhat

close to the linear elastic case. Results from finite element in the earlier chapter shows

that the pile diameter effect is insignificant for the case of linear elastic. For this

experimental study, the ratio between the largest to the smallest pile diameters was only 3.

Associated with this low ratio, an increase in the soil stiffness due to an increase of the

pile diameter based on the finding from the finite element analyses is only 25%. This

25% is relatively very small and likely could not be captured by the full-scale testing

where some other factors, such as the inhomogenity of the soil by its nature, uncertainty

in estimating the pile stiffness, some error of the determination of moment of CIDH pile

206

are more significant and can effect the accuracy of back-calculated p-y curves. As a

result, the back-calculated p-y curves show that the pile diameter has insignificant effect

up to the level of displacement tested.

However, it should be noted that the p-y curves, back-calculated from the test

results, did not reach the ultimate resistance of the soil (i.e. soil resistance seems to

increase with the displacement), especially for the smallest diameter because the yield

displacement of the pile was controlled by the pile capacity. In general, the ultimate soil

capacity increases with the pile diameter because the larger pile mobilized more soil to

achieve the ultimate soil resistance resulting in higher soil resistance per unit pile length.

At a large displacement, the pile diameter is likely to have some effect but could not be

quantified by using strain gauge data to back calculate p-y curves due to its inconsistency

at the displacement beyond the yielding of the pile.

In an attempt to back-calculate the ultimate soil resistance, an envelope of load-

displacement curves during cyclic loading was utilized. The ultimate soil pressure of

each pile was estimated by extrapolating the final slope of the p-y curves of each pile to

the displacement of 3D/80 as used in the standard sand p-y curves (Reese et al. 1974).

The soil pressure at this displacement level represents the ultimate soil resistance. In

order to verify this assumption of the ultimate soil resistance, these p-y curves were

implemented to predict the load-displacement curves in the inelastic range. Figure 6.29

through Figure 6.33 present a comparison between computed and measured load-

displacement curves of various pile diameters. It was found that the envelope of

measured load-displacement curves could be well predicted using the p-y curves with the

previous assumed ultimate soil resistance. As a result, the assumption made on the

method in estimating the ultimate soil pressure was reasonable.

It is noted that the computed load-displacement curves apparently reached failure

much earlier than that the results from the full-scale testing (Figure 6.29 through Figure

207

6.33). This is likely due to the fact that the soil confinement improved the inelastic

performance of the CIDH piles. It achieved this by retarding the spalling of unconfined

concrete and hence improved the displacement ductility of the piles. More details on

inelastic performance of CIDH pile due to the effect of soil confinement are discussed in

the next section.

Since the pile diameter appears to have insignificant effect on the p-y curves for

cemented sand before the soil reaches the ultimate soil resistance, the advantages of

increasing the pile diameter size to increase the soil resistance is negligible. However,

the benefits can be obtained in many ways as the pile diameter increases: 1) the stiffness

as well as the ultimate capacity of the pile increases and therefore decreases the

displacement response for a given lateral load, 2) for the construction point of view, it is

cost effective compared to small diameter piles with pile cap footing, and 3) using a

large diameter pile as the integral pile-shaft column can control the location of the plastic

hinge to occur at the column and thus easy to access for the rehabilitation.

6.3 Proposed Methodology to Construct p-y Curves for Weakly Cemented Sand

In this section, a methodology to construct the p-y curves for weakly cemented

sand is proposed. The methodology was developed based on the characteristics of the

back-calculated p-y curves from the experimental results. Figure 6.34 presents the

methodology for constructing p-y curves for weakly cemented sand. Since the back

calculated p-y curves at the same depth indicate that pile diameter has insignificant effect

on the p-y curves, the characteristic of proposed p-y curves for different pile diameter

below the ultimate soil resistance can be represented using a single backbone p-y curve.

The characteristic backbone curve can be estimated using the following expressions

5.0Cyp = (6.25)

208

where 50*102 += zC , and C < 415 kN/m3/2

where, p = soil resistance per unit pile length in kN/m, y = soil displacement in mm, C is

depth dependent constant, and z is depth in meter. It is noted that these expressions are

valid only when the suggested units are used. The ultimate soil resistance is determined

by adopting a suggestion by Reese et al. (1974) in which the soil reaches its ultimate

resistance at a displacement of 3D/80.

Figure 6.35 and Figure 6.36 present examples of characteristic shape of the p-y

curves developed based on the proposed methodology. Figure 6.35 shows that the soil

resistance increases as the depth increases. Figure 6.36 presents the p-y curves of

different pile diameters, which indicates that the pile diameter has no effect on the p-y

curves below the ultimate soil pressure.

The proposed p-y curves were verified by implementing them to predict the test

results for all pile diameters tested. The p-y curves were first simplified using the

quadruple-linear model in order to incorporate these p-y curves in a computer program

for analyzing lateral pile response, LPILE (Reese et al. 2000). Figure 6.37 through

Figure 6.40 show that p-y curves developed based on the proposed methodology can well

predict the response of piles under lateral loading for all pile diameters, which indicates

the accuracy of proposed p-y curves for predicting lateral pile response in weakly

cemented sand.

6.4 Limitation of Proposed p-y Curves for Design

Though the earlier section shows that the proposed methodology to construct p-y

curves for weakly cemented sand is simple and reasonable to analyze the pile response

for a wide range of pile diameters in weakly cemented, some limitations in implementing

this method should be noted. The proposed p-y curves were developed based on the full-

scale test results in weakly cemented sand with the SPT N-values of approximately 40.

209

Using these p-y curves for cemented sand material with SPT N-values more than 40

would likely underestimate the soil response. Typical SPT N-Values for cemented sand

along the coast of Southern California is often greater than 50, and therefore these p-y

curves are generally conservative for most cases.

In addition, for a case of pile diameter larger than the test pile, extrapolation of

proposed p-y curves may be reasonable, if the pile is long enough that it behaves as a

flexible pile (i.e., the lateral response is independent of depth). This is because the

derivation of p-y curves was developed based on that assumption. However, in several

cases, particularly for a case of very large pile diameter, the pile length is often relatively

short compared to the pile diameter. In this regard, the pile behaves like a rigid pile,

where the pile response depends on the pile length. Implementing these p-y curves for

this type of problem is not recommended at this stage due to unavailability of test data on

short piles. Further full-scale lateral load tests on short piles are recommended to provide

better understanding on the behavior of rigid piles.

6.5 Effect of External Confinement from Soil on Bending Behavior

The test results in earlier chapter shows that even the amount of transverse

reinforcement was lower than that suggested by BDS, it can provide sufficient inelastic

performance of the CIDH piles with the displacement ductility of more than 5 due to the

effect of soil confinement. Furthermore, the previous analyses in section 6.2.3 showed

that the numerical soil-pile system model based on the common moment-curvature

relationship, which did not account for external pressure from the soil, predicted the

failure of the pile much earlier than what observed from the test results. This effect from

the soil confinement should be therefore incorporated properly in the analyses in order to

yield the reasonable prediction of the inelastic pile response.

In this section, the soil confinement effect was incorporated by using the

equivalent amount of transverse reinforcement to represent this effect by increasing the

210

ultimate curvature of the pile until the computed load-displacement curves using

modified moment-curvature relationship matched with the experimental results. An

increase in the amount of transverse reinforcement compared to the original amount can

be used as an indicator to quantify how much the soil confinement contributes in

enhancing the ductility of the pile.

In this study, two piles tested to failure were first considered (i.e., 0.4-m and 0.6-

m piles). Figure 6.41 presents the moment-curvature relationship for both piles before

and after incorporated the soil confinement effect. The ultimate curvatures of the piles

needed to be increased by approximately 1.7 times in order to match the measured

responses. Figure 6.42 and Figure 6.43 show a good agreement between the measured

and computed load-displacement curves using the modified moment-curvature analysis.

It was found that in order to achieve the ultimate curvature ductility as presented in

Figure 6.41, the amount of transverse reinforcement for both piles needed to be increased

by approximately 100 % from the original amount of 0.6% to 1.3%. This indicates that

the effect of the soil confinement for this type of soil was equivalent to the additional

0.7% transverse reinforcement (i.e., 1.3 %-0.6% = 0.7%), which relatively high compared

to the original amount of transverse reinforcement being used. Neglecting this effect is

obviously too conservative in predicting the displacement ductility capacity of the pile.

The analyses were further conducted to predict the inelastic behavior of the 0.9-m

and 1.2-m piles, which did not reach the failure during the test due to the limitation of the

testing, by using the equivalent transverse reinforcement of 0.7% to model the soil

confinement. Figure 6.44 shows the modified moment-curvature relationship, which

incorporated the effect of soil confinement together with the unmodified moment-

curvature relationship. Figure 6.45 through Figure 6.46 shows the predicted response

using the modified moment-curvature curves with the experimental test results. It was

found that the displacement ductility at the failure of the 0.9-m and 1.2-m (No.1) piles

were more than 7.

211

The analyses show that the soil confinement can enhance the inelastic behavior of

the CIDH piles by increasing its curvature ductility due to the effect of soil confinement.

The confinement from dense weakly cemented sand considered in this test could be

considered as the equivalent transverse reinforcement ratio of 0.7%. For other types of

soils, this effect will be different depending on their strength characteristics. The softer

the soil is, the lower the amount of equivalent transverse reinforcement from the soil

confinement. For extremely soft soil such as liquefied soil or very soft clay, the effect of

soil confinement is likely to be insignificant and therefore the relationship between soil

strength and equivalent amount of transverse reinforcement can be plotted as shown in

Figure 6.47. Further full-scale experiment should be considered for evaluation of this

effect on other different soil types to determine the relationship of the amount of

equivalent transverse reinforcement with the soil strength. Implementation of this

finding into design should be done carefully due to the limitation of data available at this

current stage.

6.6 Commentary on Effect of External Confinement from Soil on Shear Capacity of CIDH Pile

In general, traditional analyses of laterally loaded CIDH piles show that a large

shear demand develops below the plastic hinge region. This is particularly true in stiff

soils, where the maximum moment that forms the plastic hinge rapidly drops to zero.

Associated with this rapid drop in moment is a high shear demand below the plastic hinge.

Using current Caltrans design methodology, this high shear demand results in increased

spiral reinforcement in the CIDH pile to a depth of several pile diameters. This increase

in reinforcement not only increases construction cost, but adversely affects the

constructability of the pile, with the additional reinforcement preventing uniform flow of

wet concrete.

The current methodology neglects any contribution to the shear capacity of the

CIDH pile from the surrounding soil. The soil contribution can be significant, especially

212

in stiff soils where the shear demand is the highest. Figure 6.48 shows the results from a

lateral load test of a 0.6-m diameter CIDH pile. Figure 6.48a shows the moment

distribution in the pile using back-calculated p-y curves from the test data. Figure 6.48b

shows the strain in the longitudinal reinforcement, showing the yielding of the

reinforcement in the plastic hinge region. Figure 6.48c shows the shear demand

calculated from the moment distribution, indicating a large shear demand just below the

plastic hinge. However, the development of this high shear is not indicated from the

strain on the transverse reinforcement because the shear capacity of the pile is much

greater than the shear force applied to the pile. It should be noted that the pile was

intentionally designed to fail by the bending mode by ensuring that the shear capacity of

the pile was larger than the shear demand. Figure 6.49 shows a comparison of shear

force that the pile experienced during the testing with the shear capacity of the CIDH pile

provided by the contributions of concrete and transverse reinforcing steel. Theoretical

shear strength using an approach of Priestley et al. (1996) in case of no axial load is given

by

scd VVV += (6.26)

)8.0('grosscc AfkV = (6.27)

θπ cot2

'

sDfA

V yhhs = (6.28)

where Vd is ideal shear strength, Vc is concrete shear-resisting mechanism, Vs is

transverse reinforcement shear resisting mechanism, k depends on the member

displacement ductility,µ , reducing from 0.29 MPa for µ < 2 to 0.05 for µ >8, Agross is

cross section area, D’ is the core dimension, θ = 30o, Ah is area of transverse bar, and fyh

is yield strength of transverse bar.

It is clearly seen that the shear force that the pile experienced is lower than the

shear capacity provided by the concrete. As a result, the contribution of shear capacity

213

provided from the transverse reinforcement is insignificant since the transverse steel did

not started to mobilize as indicated by the small strain in the transverse reinforcement.

However, the test results on the inelastic behavior of CIDH piles in the earlier

section show that the soil contribution is significant in enhancing the bending behavior of

CIDH piles. This soil confinement effect is expected to improve the shear capacity of the

pile, as well by retarding the spalling of the concrete at location where the shear demand

is the highest. Therefore, research on this area should be further investigated. In the

research, the test pile should be designed to fail under shear by ensuring the bending

capacity of the pile is greater than the shear capacity. The test pile should be extensively

instrumented with the strain gauges on both vertical and transverse reinforcements to

evaluate the effect of soil confinement in enhancing the shear capacity of the piles. The

expected benefit is design recommendations for reduced shear reinforcement in CIDH

piles resulted in decreased construction costs.

6.7 Summary

A comparison between the measured and computed natural frequencies based on

three different concepts of initial modulus of subgrade reaction showed that the pile

diameter appears to have insignificant effect on initial modulus of subgrade reaction.

Damping ratios of the soil-pile system at small strain estimated using the expression

proposed by Gazetas (1991) yielded the conservative values when compared to the

measured values obtained from the vibration testing.

The p-y curves back-calculated from the results of lateral pile load tests in weakly

cemented sand revealed that some soil resistance was observed at the ground surface

likely due to the cohesion of the soil. This is different from the characteristic of p-y

curves for clean sand as proposed by Reese et al. 1974 and API 1987 where there is no

soil resistance at the ground surface due to the lack of soil confinement. A comparison

of back-calculated p-y curves for different pile diameters indicated that pile diameter has

214

insignificant effect on the p-y curves before the soil reaches its ultimate resistance.

Results from additional analyses to predict the pile response in the inelastic range shows

that the ultimate soil pressure increases as the pile diameter increases.

Based on the characteristic of back-calculated p-y curves, the methodology to

construct the p-y curves for weakly cemented soil tested at the test site was proposed.

The p-y curves of various pile diameters can be represented by using a single backbone

curve with varying the ultimate soil pressure with the diameter. The ultimate soil

resistance was estimated using the soil pressure at the displacement of 3D/80 as

suggested by Reese et al. (1974). Good agreement between measured and computed pile

response using the proposed p-y curves validated the use of proposed p-y curves to

predict the lateral pile responses. The proposed p-y curves provided in this study were

however appropriate for the weakly cemented soil with the SPT N-values of greater than

40.

The effect of external confinement from soil was evaluated by increasing the

curvature ductility of the moment-curvature relationship until the predicted lateral pile

response matched with the actual pile behavior measured during the testing. Analyses

showed that the effect of soil confinement for dense weakly cemented soil was equivalent

to an additional amount of transverse reinforcement of 0.7%, which was greater than the

amount of transverse reinforcement of 0.6% being used in the tested piles. Neglecting

soil confinement effect appears to be too conservative in estimate the inelastic pile

performance.

215

Table 6.1 Summary of Pile and Soil Properties Used in Natural Frequency Computation for Simple Two-Layer Soil System

Pile

Flexural Soil Spring Stiffness, Ks (MN/m)

Pile Rigidity Based on Kind Based on Kdep Based on Kfin

Diameter EpIp Concept Concept Concept

(m) (MN-m2) 1st layer

2nd layer

1st layer

2nd layer

1st layer

2nd layer

0.4 40 83 288 33 115 24 82

0.6 238 " " 50 173 28 96

0.9 1,217 " " 75 259 32 111

1.2 3,530 " " 100 346 35 123

Table 6.2 Summary of Measured and Computed Natural Frequency for Simple 2-Layer System

Pile Natural Frequency (Hz) Ratio of Computed to

Diameter Additional Computed Measured Measured Natural Frequency

(m) Mass Kdep Kind Kfin Kdep Kind Kfin

0.4 No 11.3 13.6 12.8 13.6 0.84 1.01 0.94 Yes 10.9 13.0 12.2 12.5 0.87 1.04 0.98

0.6 No 16.3 18.2 17.5 18.1 0.90 1.01 0.97 0.9 Yes 25.5 26.2 25.9 25.9 0.99 1.01 1.00

1.2 (No.1) No 36.1 34.0 35.7 34.5 1.05 0.99 1.04 Yes 35.2 33.2 33.9 33.5 1.05 0.99 1.01

1.2 (No.2) No 33.9 32.0 32.7 32.4 1.05 0.99 1.01 Yes 33.1 31.3 31.9 32.1 1.03 0.98 1.00

216

12 m

1.5x1.5x0.75m Load Stub

Ks1 /2

ModelPrototype

Ks1 @ 0.15 mspacing

vs = 315 m/s

vs = 560 m/s

Ks2 @ 0.15 mspacing

Lumped Mass

6 m

6 m

Soil Layer 1

Soil Layer 2

Figure 6.1 Numerical Soil-Pile System Model for Simple Two-Layer System

217

2520151050Depth (m)

010

2030

4050

Trav

el T

ime

(ms)

2-La

yer S

yste

mSt

iffne

ss In

crea

sing

with

Dep

th

(b)

2520151050

Depth (m)

020

040

060

080

0

Shea

r Wav

e Ve

loci

ty (m

/s)

2-La

yer S

yste

mSt

iffne

ss In

crea

sing

with

Dep

th

(a)

315

m/s

560

m/s

Figu

re 6

.2

Det

erm

inat

ion

of S

hear

Wav

e V

eloc

ity P

rofil

e (a

) Tra

vel T

ime

Plot

and

(b) S

hear

Wav

e V

eloc

ity

218

0 0.5 1 1.5 2Pile Diameter (m)

0

0.5

1

1.5

Rat

io o

f Com

pute

d to

Mea

sure

d N

atur

al F

requ

ency

KindKdep

Simple Two-Layer Soil Profile

Kdep( based on parametric study)

Kind

Kdep

Figure 6.3 Ratio of Computed to Measure Natural Frequency vs. Pile Diameter for Simple Two-Layer Soil Profile (Kind vs. Kdep)


0

0.5

1

1.5

Rat

io o

f Com

pute

d to

Mea

sure

d N

atur

al F

requ

ency

KindKfin

Simple Two-Layer Soil Profile

Kind

Kfin

Figure 6.4 Ratio of Computed to Measure Natural Frequency vs. Pile Diameter for Simple Two-Layer Soil Profile (Kind vs. Kfin)

219


0

0.5

1

1.5

Rat

io o

f Com

pute

d to

Mea

sure

d N

atur

al F

requ

ency

KindKdepKfin

Increasing Stiffness with Depth Soil Profile

Kind

Kdep

Kfin

Figure 6.5 Ratio of Computed to Measure Natural Frequency vs. Pile Diameter for Increasing Stiffness with Depth Soil Profile


0

0.5

1

1.5

Rat

io o

f Com

pute

d to

Mea

sure

d N

atur

al F

requ

ency

KindKdepKfin

Increasing Stiffness with Depth Soil Profile

Kind

Kdep

Kfin

Figure 6.6 Ratio of Computed to Measure Natural Frequency vs. Pile Diameter for Increasing Stiffness with Depth Soil Profile (After increasing soil spring stiffnesses)

220

0 10 20 30 40Natural Frequency (Hz)

0

10

20

30

Dam

ping

Rat

io (%

)

MeasuredComputed

Figure 6.7 Comparison of Measured and Computed Damping Ratios

221

-3000

-2000

-1000

0

1000

2000

3000

Stra

in (x

10-6

)

-800 -400 0 400 800Distance from Center (mm)

Curvature(φ) = Slope(dε/ds)

Figure 6.8 Example of Curvature Calculation from Strain Gauge Data (Extracted Data from 1.2-m CIDH Pile (No-1))

222

0 0.04 0.08 0.12 0.16 0.2Curvature (1/m)

0

40

80

120

160

200

Mom

ent (

kN.m

)

from UCFyber AnalysisSimplified

0 0.01 0.02 0.03Curvature (1/m)

0

40

80

120

160

Mom

ent (

kN.m

)


(a)

(b)

Figure 6.9 Moment-Curvature Relationships for 0.4-m CIDH Pile (a) Entire Curve, and (b) Before Yielding

223

0 0.02 0.04 0.06 0.08 0.1Curvature (1/m)

0

200

400

600

800

Mom

ent (

kN.m

)


0 0.004 0.008 0.012 0.016Curvature (1/m)

0

200

400

600

Mom

ent (

kN.m

)


(a)

(b)


224

0 0.02 0.04 0.06 0.08Curvature (1/m)

0

500

1000

1500

2000

2500

3000

Mom

ent (

kN.m

)


0 0.002 0.004 0.006 0.008Curvature (1/m)

0

500

1000

1500

2000

2500

Mom

ent (

kN.m

)


(a)

(b)


225

0 0.01 0.02 0.03 0.04 0.05 0.06Curvature (1/m)

0

1000

2000

3000

4000

5000

6000

7000

Mom

ent (

kN.m

)


0 0.002 0.004 0.006 0.008 0.01Curvature (1/m)

0

1000

2000

3000

4000

5000

6000

Mom

ent (

kN.m

)


(a)

(b)


226

0 4 8 12 16 20Soil Displacement, y (mm)

0

100

200

300

Soil

Pres

sure

, p (k

N/m

)

0 m0.15 m0.30 m0.46 m0.61 m0.76 m

Figure 6.13 Back-Calculated p-y Curves for 0.4-m CIDH Pile

227

010

2030

40D

ispl

acem

ent (

mm

)

04080120

160

Load (kN)

Mea

sure

dC

ompu

ted

040

8012

016

0M

omen

t (kN

-m)

43210-1

Depth (m)

20 k

N (M

easu

red)

40 k

N (M

easu

red)

60 k

N (M

easu

red)

80 k

N (M

easu

red)

100

kN (M

easu

red)

120

kN (M

easu

red)

138

kN (M

easu

red)

Com

pute

d

(a)

(b)

Figu

re 6

.14

Com

paris

on o

f Tes

t Res

ults

and

Ana

lysi

s Usi

ng B

ack-

Cal

cula

ted

p-y

Cur

ves f

or 0

.4-m

CID

H P

ile (

a) L

oad-

Dis

plac

emen

t Cur

ve, a

nd (b

) Mom

ent P

rofil

es

228

010

2030

40D

ispl

acem

ent (

mm

)

43210-1

Depth (m)

20 k

N (M

easu

red)

40 k

N (M

easu

red)

60 k

N (M

easu

red)

80 k

N (M

easu

red)

100

kN (M

easu

red)

120

kN (M

easu

red)

138

kN (M

easu

red)

Com

pute

d

-0.0

25-0

.02

-0.0

15-0

.01

-0.0

050

Rot

atio

n (R

adia

n)

43210-1Depth (m)

20 k

N (M

easu

red)

40 k

N (M

easu

red)

60 k

N (M

easu

red)

80 k

N (M

easu

red)

100

kN (M

easu

red)

120

kN (M

easu

red)

138

kN (M

easu

red)

Com

pute

d

(a)

(b)

Figu

re 6

.15

Com

paris

on o

f Tes

t Res

ults

and

Ana

lysi

s Usi

ng B

ack-

Cal

cula

ted

p-y

Cur

ves f

or 0

.4-m

CID

H P

ile (

a) R

otat

ion

Prof

iles,

and

(b) D

ispl

acem

ent

Prof

iles

229

0 10 20 30Soil Displacement, y (mm)

0

200

400

600

Soil

Pres

sure

, p (k

N/m

)

0 m0.15 m0.30 m0.46 m0.61 m0.76 m0.91 m1.07 m

Depth


230

020

4060

Dis

plac

emen

t (m

m)

0

100

200

300

400

Load (kN)

Mea

sure

dC

ompu

ted

020

040

060

080

0M

omen

t (kN

-m)

121086420-2

Depth (m)

30 k

N (M

easu

red)

94 k

N (M

easu

red)

150

kN (M

easu

red)

257

kN (M

easu

red)

340

kN (M

easu

red)

Com

pute

d

(a)

(b)

Figu

re 6

.17

Com

paris

on o

f Tes

t Res

ults

and

Ana

lysi

s Usi

ng B

ack-

Cal

cula

ted

p-y

Cur

ves f

or 0

.6-m

CID

H P

ile (

a) L

oad-

Dis

plac

emen

t Cur

ve, a

nd (b

) Mom

ent P

rofil

es

231

020

4060

Dis

plac

emen

t (m

m)

121086420-2

Depth (m)

30 k

N (M

easu

red)

94 k

N (M

easu

red)

150

kN (M

easu

red)

257

kN (M

easu

red)

340

kN (M

easu

red)

Com

pute

d

-0.0

3-0

.02

-0.0

10

Rot

atio

n (R

adia

n)

121086420-2

Depth (m)

30 k

N (M

easu

red)

94 k

N (M

easu

red)

150

kN (M

easu

red)

257

kN (M

easu

red)

340

kN (M

easu

red)

Com

pute

d

(a)

(b)

Figu

re 6

.18

Com

paris

on o

f Tes

t Res

ults

and

Ana

lysi

s Usi

ng B

ack-

Cal

cula

ted

p-y

Cur

ves f

or 0

.6-m

CID

H P

ile (

a) R

otat

ion

Prof

iles,

and

(b) D

ispl

acem

ent

Prof

iles

232


0

200

400

600

800

1000

Soil

Pres

sure

, p (k

N/m

)

0 m0.30 m0.61 m0.91 m1.22 m1.52 m1.83 m2.13 m2.44 m

Depth


233

020

4060

80D

ispl

acem

ent (

mm

)

0

200

400

600

800

1000

1200

Load (kN)

Mea

sure

dC

ompu

ted

040

080

012

0016

0020

00M

omen

t (kN

-m)

121086420-2

Depth (m)

214

kN (M

easu

red)

423

kN (M

easu

red)

636

kN (M

easu

red)

845

kN (M

easu

red)

Com

pute

d

(a)

(b)

Figu

re 6

.20

Com

paris

on o

f Tes

t Res

ults

and

Ana

lysi

s Usi

ng B

ack-

Cal

cula

ted

p-y

Cur

ves f

or 0

.9-m

CID

H P

ile (

a) L

oad-

Dis

plac

emen

t Cur

ve, a

nd (b

) Mom

ent P

rofil

es

234

020

4060

Dis

plac

emen

t (m

m)

121086420-2

Depth (m)

214

kN (M

easu

red)

423

kN (M

easu

red)

636

kN (M

easu

red)

845

kN (M

easu

red)

Com

pute

d

-0.0

2-0

.015

-0.0

1-0

.005

0R

otat

ion

(Rad

ian)

121086420-2

Depth (m)

214

kN (M

easu

red)

423

kN (M

easu

red)

636

kN (M

easu

red)

845

kN (M

easu

red)

Com

pute

d

(a)

(b)

Figu

re 6

.21

Com

paris

on o

f Tes

t Res

ults

and

Ana

lysi

s Usi

ng B

ack-

Cal

cula

ted

p-y

Cur

ves f

or 0

.9-m

CID

H P

ile (

a) R

otat

ion

Prof

iles,

and

(b) D

ispl

acem

ent

Prof

iles

235

0 10 20 30 40 50 60Soil Displacement, y (mm)

0

200

400

600

800

1000

1200

1400

Soil

Pres

sure

, p (k

N/m

)

0 m0.30 m0.61 m0.91 m1.22 m1.52 m1.83 m2.13 m2.44 m2.74 m

Depth

Figure 6.22 Back-Calculated p-y Curves for 1.2-m CIDH Pile (No.1)

236

020

4060

80D

ispl

acem

ent (

mm

)

0

400

800

1200

1600

2000

Load (kN)

Mea

sure

dC

ompu

ted

020

0040

0060

00M

omen

t (kN

-m)

121086420-2

Depth (m)

214

kN (M

easu

red)

423

kN (M

easu

red)

636

kN (M

easu

red)

845

kN (M

easu

red)

1059

kN

(Mea

sure

d)14

32 k

N (M

easu

red)

1717

kN

(Mea

sure

d)19

48 k

N (M

easu

red)

Com

pute

d

(a)

(b)

Figu

re 6

.23

Com

paris

on o

f Tes

t Res

ults

and

Ana

lysi

s Usi

ng B

ack-

Cal

cula

ted

p-y

Cur

ves f

or 1

.2-m

CID

H P

ile (N

o.1)

(a)

Lo

ad-D

ispl

acem

ent C

urve

, and

(b) M

omen

t Pro

files

237

020

4060

80D

ispl

acem

ent (

mm

)

121086420-2

Depth (m)

214

kN (M

easu

red)

423

kN (M

easu

red)

636

kN (M

easu

red)

845

kN (M

easu

red)

1059

kN

(Mea

sure

d)14

32 k

N (M

easu

red)

1717

kN

(Mea

sure

d)19

48 k

N (M

easu

red)

Com

pute

d

-0.0

2-0

.015

-0.0

1-0

.005

0R

otat

ion

(Rad

ian)

121086420-2

Depth (m)

214

kN (M

easu

red)

423

kN (M

easu

red)

636

kN (M

easu

red)

845

kN (M

easu

red)

1059

kN

(Mea

sure

d)14

32 k

N (M

easu

red)

1717

kN

(Mea

sure

d)19

48 k

N (M

easu

red)

Com

pute

d

(a)

(b)

Figu

re 6

.24

Com

paris

on o

f Tes

t Res

ults

and

Ana

lysi

s Usi

ng B

ack-

Cal

cula

ted

p-y

Cur

ves f

or 1

.2-m

CID

H P

ile (N

o.1)

(a)

Rot

atio

n Pr

ofile

s, an

d (b

) Dis

plac

emen

t Pr

ofile

s

238

0 10 20 30 40 50 60Soil Displacement, y (mm)

0

200

400

600

800

1000

Soil

Pres

sure

, p (k

N/m

)

0 m0.30 m0.61 m0.91 m1.22 m1.52 m1.83 m2.13 m2.44 m2.74 m

Depth

Figure 6.25 Back-Calculated p-y Curves for 1.2-m CIDH Pile (No.2)

239

020

4060

8010

0D

ispl

acem

ent (

mm

)

0

400

800

1200

1600

2000

Load (kN)

Mea

sure

dC

ompu

ted

020

0040

0060

00M

omen

t (kN

-m)

121086420-2

Depth (m)

285

kN (M

easu

red)

574

kN (M

easu

red)

858

kN (M

easu

red)

1148

kN

(Mea

sure

d)14

32 k

N (M

easu

red)

1717

kN

(Mea

sure

d)C

ompu

ted

(a)

(b)

Figu

re 6

.26

Com

paris

on o

f Tes

t Res

ults

and

Ana

lysi

s Usi

ng B

ack-

Cal

cula

ted

p-y

Cur

ves f

or 1

.2-m

CID

H P

ile (N

o.2)

(a)

Lo

ad-D

ispl

acem

ent C

urve

, and

(b) M

omen

t Pro

files

240

020

4060

8010

0D

ispl

acem

ent (

mm

)

121086420-2

Depth (m)

285

kN (M

easu

red)

574

kN (M

easu

red)

858

kN (M

easu

red)

1148

kN

(Mea

sure

d)14

32 k

N (M

easu

red)

1717

kN

(Mea

sure

d)C

ompu

ted

-0.0

25-0

.02

-0.0

15-0

.01

-0.0

050

Rot

atio

n (R

adia

n)

121086420-2

Depth (m)

285

kN (M

easu

red)

574

kN (M

easu

red)

858

kN (M

easu

red)

1148

kN

(Mea

sure

d)14

32 k

N (M

easu

red)

1717

kN

(Mea

sure

d)C

ompu

ted

(a)

(b)

Figu

re 6

.27

Com

paris

on o

f Tes

t Res

ults

and

Ana

lysi

s Usi

ng B

ack-

Cal

cula

ted

p-y

Cur

ves f

or 1

.2-m

CID

H P

ile (N

o.2)

(a)

R

otat

ion

Prof

iles,

and

(b) D

ispl

acem

ent

Prof

iles

241

0 20 40 60y (mm)

0

200

400

600

800

p (k

N/m

)0.4-m Pile0.6-m Pile0.9-m Pile1.2-m Pile (No.1)1.2-m Pile (No.2)

0 20 40 60y (mm)

0

200

400

600

800

p (k

N/m

)

0 20 40 60y (mm)

0

200

400

600

800

p (k

N/m

)

0 20 40 60y (mm)

0

200

400

600

800

p (k

N/m

)

0 20 40 60y (mm)

0

200

400

600

800

p (k

N/m

)

Depth 0 m Depth 0.3 m

0 20 40 60y (mm)

0

200

400

600

800

p (k

N/m

)

Depth 0.6 m Depth 0.9 m


Figure 6.28 Comparison of p-y Curves for Different Pile Diameters at Various Depths

242

-300 -200 -100 0 100 200 300Displacement (mm)

-300

-200

-100

0

100

200

300

Load

(kN

)

CyclicStaticComputed

Push

Pull

1.7 2.32.9 3.5 4.6 5.8 6.9µ∆

Figure 6.29 Comparison between Measured and Computed Load-Displacement Curves in Inelastic Range for 0.4-m CIDH Pile

-400 -200 0 200 400Displacement (mm)

-600

-400

-200

0

200

400

600

Load

(kN

)


Push

Pull1.9 2.6 3.8 5.0 6.4 7.48.1µ∆


243

-600 -400 -200 0 200 400 600Displacement (mm)

-2000

-1500

-1000

-500

0

500

1000

1500

2000

Load

(kN

)


Push

Pull

2.22.8

3.4 4.5 5.6 7.6 8.71.7µ∆


-600 -400 -200 0 200 400 600Displacement (mm)

-3000

-2000

-1000

0

1000

2000

3000

Load

(kN

)


Push

Pull

Figure 6.32 Comparison between Measured and Computed Load-Displacement Curves in Inelastic Range for 1.2-m CIDH Pile (No.1)

244

-600 -400 -200 0 200 400 600Displacement (mm)

-3000

-2000

-1000

0

1000

2000

3000

Load

(kN

)


Push

Pull

2.1 4.1 5.2 6.2µ∆

Figure 6.33 Comparison between Measured and Computed Load-Displacement Curves in Inelastic Range for 1.2-m CIDH Pile (No.2)

245

Soil Displacement, y (mm)

Soil

Pres

sure

, p (k

N/m

)

3D1/80

Pult for D1

3D2/80

Pult for D2

p = Cy0.5, p in kN/m, y in mm where, C = 102*Z+50 but < 415, Z = Depth (m)

Pult for D3

3D3/80

Figure 6.34 Proposed Methodology for Constructing p-y Curves for Weakly Cemented Sand

246


0

200

400

600

800

1000

Soil

Pres

sure

, p (k

N/m

)

0 m

0.3 m

0.6 m

0.9 m

1.2 m

1.5 m

Depth

Figure 6.35 Example of Characteristic of Proposed p-y Curves for 0.4-m Pile at Various Depths

0 20 40 60Soil Displacement, y (mm)

0

400

800

1200

Soil

Pres

sure

, p (k

N/m

)

D = 0.4 m

D = 0.6 m

D = 0.9 m

D = 1.2 m

4 Lines

Figure 6.36 Example of Characteristic of Proposed p-y Curves for Various Pile Diameters at Depth of 0.9 m

247

010

2030

40D

ispl

acem

ent (

mm

)

04080120

160

Load (kN)

Mea

sure

dC

ompu

ted

040

8012

016

0M

omen

t (kN

-m)

43210-1

Depth (m)

20 k

N (M

easu

red)

60 k

N (M

easu

red)

100

kN (M

easu

red)

138

kN (M

easu

red)

Com

pute

d

(a)

(b)

Figu

re 6

.37

Com

paris

on o

f Tes

t Res

ults

and

Ana

lysi

s Usi

ng P

ropo

sed

p-y

Cur

ves f

or 0

.4-m

CID

H P

ile (

a) L

oad-

Dis

plac

emen

t Cur

ve, a

nd (b

) Mom

ent P

rofil

es

248

020

4060

Dis

plac

emen

t (m

m)

0

100

200

300

400

Load (kN)

Mea

sure

dC

ompu

ted

020

040

060

0M

omen

t (kN

-m)

121086420-2

Depth (m)

30 k

N (M

easu

red)

94 k

N (M

easu

red)

150

kN (M

easu

red)

257

kN (M

easu

red)

Com

pute

d

(a)

(b)

Figu

re 6

.38

Com

paris

on o

f Tes

t Res

ults

and

Ana

lysi

s Usi

ng P

ropo

sed

p-y

Cur

ves f

or 0

.6-m

CID

H P

ile (

a) L

oad-

Dis

plac

emen

t Cur

ve, a

nd (b

) Mom

ent P

rofil

es

249

020

4060

80D

ispl

acem

ent (

mm

)

0

200

400

600

800

1000

1200

Load (kN)

Mea

sure

dC

ompu

ted

040

080

012

0016

0020

00M

omen

t (kN

-m)

121086420-2

Depth (m)

214

kN (M

easu

red)

423

kN (M

easu

red)

636

kN (M

easu

red)

845

kN (M

easu

red)

Com

pute

d

(a)

(b)

Figu

re 6

.39

Com

paris

on o

f Tes

t Res

ults

and

Ana

lysi

s Usi

ng P

ropo

sed

p-y

Cur

ves f

or 0

.9-m

CID

H P

ile (

a) L

oad-

Dis

plac

emen

t Cur

ve, a

nd (b

) Mom

ent P

rofil

es

250

020

4060

80D

ispl

acem

ent (

mm

)

0

400

800

1200

1600

2000

Load (kN)

Mea

sure

dC

ompu

ted

020

0040

0060

00M

omen

t (kN

-m)

121086420-2

Depth (m)

423

kN (M

easu

red)

845

kN (M

easu

red)

1432

kN

(Mea

sure

d)19

48 k

N (M

easu

red)

(a)

(b)

Figu

re 6

.40

Com

paris

on o

f Tes

t Res

ults

and

Ana

lysi

s Usi

ng P

ropo

sed

p-y

Cur

ves f

or 1

.2-m

CID

H P

ile (

No.

1) (a

) Loa

d-D

ispl

acem

ent C

urve

, and

(b) M

omen

t Pro

files

251

0 0.1 0.2 0.3Curvature (1/m)

0

40

80

120

160

200

Mom

ent (

kN.m

)

Without Soil Confinement EffectModified for Soil Confinement Effect

a) 0.4-m Pile

0 0.05 0.1 0.15 0.2Curvature (1/m)

0

200

400

600

800

Mom

ent (

kN.m

)

Without Soil Confinement EffectModified for SoilConfinement Effect

b) 0.6-m Pile

Ultimate

Ultimate

Figure 6.41 Modified Moment-Curvature Relationships for Effect of Soil Confinement (a) 0.4-m Pile, and (b) 0.6-m Pile

252

-300 -200 -100 0 100 200 300Displacement (mm)

-300

-200

-100

0

100

200

300

Load

(kN

)


Push

Pull

1.7 2.32.9 3.5 4.6 5.8 6.9µ∆

Predicted Failure Point(without Confinement)

Figure 6.42 Comparison between Measured and Computed Load-Displacement Curves using Modified Moment-Curvature Relationship for 0.4-m CIDH Pile

-400 -200 0 200 400Displacement (mm)

-600

-400

-200

0

200

400

600

Load

(kN

)


Push

Pull1.9 2.6 3.8 5.0 6.4 7.48.1µ∆



253

0 0.04 0.08 0.12Curvature (1/m)

0

500

1000

1500

2000

2500

3000

Mom

ent (

kN.m

)

Without SoilConfinement EffectModified for SoilConfinement Effect

a) 0.9-m Pile

0 0.02 0.04 0.06 0.08 0.1Curvature (1/m)

0

1000

2000

3000

4000

5000

6000

7000

Mom

ent (

kN.m

)

Without SoilConfinement EffectModified for SoilConfinement Effect

b) 1.2-m Pile

Ultimate

Ultimate

Figure 6.44 Modified Moment-Curvature Relationships for Effect of Soil Confinement (a) 0.9-m Pile, and (b) 1.2-m Pile

254

-600 -400 -200 0 200 400 600Displacement (mm)

-2000

-1500

-1000

-500

0

500

1000

1500

2000

Load

(kN

)


Push

Pull

2.22.8

3.4 4.5 5.6 7.6 8.71.7µ∆



-600 -400 -200 0 200 400 600Displacement (mm)

-3000

-2000

-1000

0

1000

2000

3000

Load

(kN

)


Push

PullPredicted Failure Point(without Confinement)

µ∆

7.8

2.9

Figure 6.46 Comparison between Measured and Computed Load-Displacement Curves using Modified Moment-Curvature Relationship for 1.2-m CIDH Pile (No.1)

255

Liquiefy Soilor Very Soft Clay

0.7%

Equi

vale

nt T

rans

vers

e R

einf

orce

men

t (%

)

0

Dense WeaklyCemented Soil

Soil Strength

?

From UCSD Test Results

?

?

Range for Further Research

Figure 6.47 Relationship of Equivalent Transverse Reinforcement due to Soil confinement

256

050

010

00M

omen

t (kN

-m)

543210 Depth (m)

Load

94 k

N15

0 kN

257

kN34

0 kN

384

kN

050

0010

000

1500

0

Long

itudi

nal S

trai

n (x

10-6)

543210-6

00-3

000

300

600

Shea

r (kN

)

543210-5

000

500

Tran

sver

se S

trai

n (x

10-6)

543210

Fi

gure

6.4

8 R

esul

ts o

f Lat

eral

Loa

d Te

st o

n 0.

6-m

Pile

257

0 2 4 6 8Displacement Ductility

0

400

800

1200

1600

Shea

r For

ce (k

N)

Theoretical Shear CapacityActual Shear Force

Shear Capacity from ConcreteShear Capacity from Transverse Steel

Figure 6.49 Comparison of Theoretical Shear Capacity with Experimentally Observed Shear

258


259

Chapter 7 IMPLEMENTATION OF EXISTING p-y CURVES FOR WEAKLY CEMENTED SAND

In this chapter, the capability of various existing p-y curves in predicting the

lateral pile response in weakly cemented sand is evaluated. Results from this portion

study can lead to valuable conclusions regarding which of the existing p-y curves are the

most appropriate and how much error would be expected when implementing these p-y

curves to analyze the pile response in weakly cemented sand. Four different types of p-y

curves that are available in engineering practice were considered in this study (i.e., sand

p-y curves, Reese et al. 1974 and API 1987; cemented sand p-y curves, Ismael 1987; silt

p-y curves, Reese and Van Impe 2001).

When analyzing pile response in weakly cemented sand, one of the most

acceptable approaches is to neglect the soil resistance from the soil cohesion component.

Implementing the sand p-y curves proposed by either Reese et al. (1974) or API (1987) is

therefore believed to be a conservative method to analyze the pile response in weakly

cemented sand. Therefore, both of them are investigated in this study.

Experimental test results of piles embedded in cemented sand in Kuwait (Ismael

1990) support the previous concept that using sand p-y curves for predicting the response

in cemented sand would be conservative. Ismael proposed the new approach in

developing p-y curves for cemented sand by incorporating the cohesion term into the

equations, which is used for determining the ultimate soil pressure. It was found that the

proposed p-y curves could be used to predict the test results with reasonable accuracy.

However, the tests were performed on a single pile diameter (0.3 m). Using the existing

p-y curves for cemented sand to predict pile response for a wide range of pile diameters is

therefore of interest and are evaluated in the following section.

260

The last p-y curves considered in this study were the silt p-y curves proposed by

Reese and Van Impe (2001), which were developed based on the concept by Ismael

(1990). The silt p-y curves incorporate the cohesion term into the sand p-y curves (Reese

et al 1974). These p-y curves were developed based on the theoretical basis alone

without any verification from full-scale testing results. A comparison of computed pile

response using the silt p-y curves with the measured pile response is useful in verifying

the accuracy of these p-y curves. Based on these analyses, suggestion for the design of

piles in weakly cemented sand is provided.

7.1 p-y Curves for Sand

The back-calculated p-y curves from the full-scale tests were compared to the

existing sand p-y curves to evaluate how well the sand p-y curves can model the behavior

of weakly cemented sand. Two types of sand p-y curves (i.e., Reese et al. 1974 and API

1987) currently available in engineering practice are considered. Sand p-y curves

proposed by Reese et al. 1974 were developed based on the results of full-scale lateral

pile load tests at Mustang Island, Houston, Texas. The methodology in constructing p-y

curves proposed by Reese et al. (1974) is tedious due to several lengthy equations

involved in estimating the ultimate soil pressure, as well as the use of more than one

function to represent the shape of the p-y curves.

O’Neill and Murchison (1983) simplified the methodology by using only a single

convenient trigonometric equation to represent the Reese’s sand p-y curves. This

suggestion was adopted by the American Petroleum Institute (API) and incorporated in

its manual on recommended practice (API 1987). One of the differences between the

sand p-y cures and the API p-y curves is the shape function of the curve; the API p-y

curves are usually stiffer.

Figure 7.1 and Figure 7.2 present a comparison of the back-calculated p-y curves

of weakly cemented sand with the sand p-y curves proposed by Reese et al. (1974) and

261

API (1987) at several depths. For the purpose of comparison, only the back-calculated p-

y curves for the 0.4-m and 1.2-m piles are presented. The soil properties were estimated

based on the corrected SPT-N values measured at the test site. Using correlation

proposed by Meyerhof (1956), the friction angle for the first 6-m was estimated as 42

degrees. Below this layer a friction angle of 45 degrees was used. The soil unit weight

was assumed as 20 kN/m3 for the entire depth. A subgrade reaction constant of 76

MN/m3 associated with the property of very dense sand was used for both layers.

As shown in Figure 7.1 and Figure 7.2, the back-calculated p-y curves for the 0.4-

m pile provides significantly higher resistance compared to both existing sand p-y curves,

especially for the first 1 meter depth. Below this depth, the displacement level of the

back-calculated p-y curves is too small and could not be well compared. No soil

resistance at the ground surface is observed for both existing sand p-y curves; whereas,

significant soil resistance is noticeable for the back-calculated p-y curves likely due to the

presence of soil cohesion.

Compared with the p-y curves for the 0.4-m pile, the sand p-y curves for the 1.2-m

pile are in better agreement with the back-calculated p-y curves, particularly at a

displacement of less than 10 mm. Beyond this range, the sand p-y curves provide less

soil resistance although the difference between those two becomes smaller as the depth

increases. Below a depth of 1.8 m the initial portions of the sand p-y curves are stiffer

than those of the back-calculated p-y curves. This is because the initial stiffness of the

sand p-y curves increases linearly with depth, whereas that of back-calculated p-y curves

increases at a slower rate.

In general, API p-y curves are somewhat stiffer than Reese’s sand p-y curves at all

depths and are in better agreement with the back-calculated p-y curves. It should be

noted that the API sand p-y curves theoretically should give the same ultimate soil

pressure as Reese’s sand p-y curves. However, Figure 7.2 shows that at some depths,

262

there are some differences in ultimate soil pressure based on different assumptions in the

respective methods. This is because corrections factor A (discussed in Chapter 2) in the

API p-y curves was more conservative at some depths, resulting in a difference in

ultimate soil pressure.

As mentioned earlier, using sand p-y curves to predict pile response in weakly

cemented sand is generally believed to be a conservative method because the cohesion of

the soil is neglected. Figure 7.3 shows a comparison of computed load-displacement

curves of each pile using the sand p-y curves to the measured load-displacement curves.

Clearly, both sand p-y curves yield the conservative computed response over the range of

the diameter tested. As expected from the comparison of p-y curves discussed earlier, the

API p-y curves are in better agreement with the experimental test results.

Interestingly, the agreement between the test results and the response predicted

using the sand p-y curves improves as the pile diameter increases. However, this trend

indicates that the sand p-y curves may tend to overestimate the pile response as the

diameter increases beyond 1.2 m. This is due to the difference in the characteristics of p-

y curves, as well as the diameter effect incorporated in the sand p-y curves appearing to

be too large for the use in cemented sand. In fact, the back-calculated p-y curves show

that the pile diameter effect on the p-y curves for cemented sand is insignificant for a

range of displacement smaller than the ultimate soil resistance.

Additional analyses were conducted to validate this finding by comparing the

load-displacement curves of a pile diameter larger than 1.2 m using the proposed p-y

curves and API sand p-y curves. This analysis was conducted based on the assumption

that the pile response obtained using the proposed p-y curves results in the measured

response in the field. This assumption appears to be reasonable because the earlier study

shows that the proposed p-y curves give an excellent agreement of pile response

compared to the experimental test data. Figure 7.4 shows that the predicted pile

263

response using the API p-y curves before the pile reaches the yield load are stiffer

compared to that computed from the proposed p-y curves, but the yield load obtained

from the API sand p-y curves are slightly lower than those obtained using the proposed p-

y curves. This finding shows that a non-conservative prediction of pile response in

weakly cemented sand may be encountered for large pile diameters, even though the sand

p-y curves, which are believed to be conservative for cemented sand, are implemented.

The ratio of predicted to measured pile responses (pile head displacement,

maximum moment, and depth to maximum moment) using the sand p-y curves proposed

by Reese et al. and API p-y curves are presented in Figure 7.5 and Figure 7.6,

respectively. In general, increasing pile diameter increases the accuracy in predicting pile

response. However, the API sand p-y curves overestimate the pile capacity as the

diameter increases to 1.8 and 2.4 m as indicated in Figure 7.6. In addition, the existing

sand p-y curves underestimate the pile head displacement about 2.5 times for the 0.4-m

pile and decrease to about 1.5 times for the1.2-m pile. The error in estimating the

maximum moment for all pile diameters studied is less than 50%, with the error being

smaller for the larger piles. The accuracy in predicting the maximum moment is

moderate with the error ranging between 10 to 80%. In general, API p-y curves appear to

yield slightly better agreement in predicting the pile response than the Reese’s sand p-y

curves, particularly for the pile head displacement.

Based on the analytical study, though conservative for small diameter piles, the

sand p-y curves seem to be inappropriate to analyze the pile response in weakly cemented

sand, especially for a large pile diameter. This is mainly due to the pile diameter effect

incorporated in the existing sand p-y curves, which appears to be too much for weakly

cemented sand. Therefore, implementing sand p-y curves to analyze the behavior of

laterally loaded piles of large pile diameters should be used with caution.

264

7.2 p-y Curves for c-φ Soil

Parametric studies in the previous section indicate that the sand p-y curves are not

appropriate for analyzing pile response in weakly cemented sand, particular for large

diameter piles. In this section, the existing cemented sand p-y curves proposed by Ismael

(1990) are compared with the back-calculated p-y curves from the full-scale tests at

diameters of 0.4m and 1.2m, as well as implemented to predict the measured pile

response for various diameters. Furthermore, the silt p-y curves proposed by Reese and

Van Impe (2001) which accounted for both cohesion and friction angle are considered in

this study.

7.2.1 Cemented Sand p-y Curves (Ismael 1990)

A review of Figure 7.7 and Figure 7.8 shows that the back-calculated p-y curves

of the 1.2-m pile favorably agree with the cemented sand p-y curves (Ismael 1990) for

most depths; whereas the back-calculated p-y curves of the 0.4-m pile are somewhat

stiffer than the Ismael p-y curves. The soil properties used in this analysis were similar to

those used for the sand p-y curves, with an addition of a soil cohesion of 20 kPa. This

cohesion corresponds to the cohesion of weakly cemented soil and is the lower bound

values obtained from the direct shear test results. Figure 7.9 shows the load-displacement

curves obtained by using cemented sand p-y curves compared to the full-scale test results.

Good agreement is observed for the 1.2-m pile. However, the predicted pile response

decreases in accuracy as the pile diameter decreases, yet in a more conservative way.

The ratio of pile response using cemented sand p-y curves to the pile response

obtained by using the proposed p-y curves is presented in Figure 7.10. As expected,

cemented sand p-y curves generally yield better prediction of pile response than both

sand p-y curves implemented in the previous section. It is likely due to the fact that the

p-y curves using Ismael methodology can better represent the characteristics of weakly

cemented sand, in which these p-y curves shows some soil resistance at ground surface;

265

whereas there is no soil resistance observed for the sand p-y curves. However, the pile

diameter effect incorporated in these p-y curves is still somewhat inappropriate. As

observed in Figure 7.10, the agreement of pile response improves as the pile diameter

increases for the range of diameter tested. Again, using these p-y curves for a large pile

diameter tends to overestimate the actual pile response. This is confirmed by additional

parametric analyses on larger pile diameters (i.e. 1.8 m and 2.4 m).

Among comparisons of the pile response using cemented sand p-y curves, the

error in estimating the maximum moment appears to be the smallest with the error being

less than 10% for all pile diameters. The errors in estimating the depth to maximum

moment and pile head displacement are moderate and the highest, respectively. If one

considers only the magnitude of maximum moment for a design, cemented sand p-y

curves can give a reasonable estimation.

7.2.2 p-y Curves for Silt (Reese and Van Impe 2001)

Silt p-y curves (Reese and Van Impe 2001) of the 0.4-m and 1.2-m piles were

developed using the soil properties used in Ismael p-y curves. Figure 7.11 and Figure

7.12 present a comparison between the back-calculated p-y curves and silt p-y curves at

several depths. Though the cohesion term was incorporated into the equations used to

compute the ultimate soil pressure, the silt p-y curves do not show any soil resistance at

ground surface. Results in implementing the silt p-y curves to predict the pile response

for various pile diameters are presented in Figure 7.13. Good agreement between the

computed response using silt p-y curves and the test results is observed for the 1.2-m pile.

Again, a more conservative response was observed as the pile diameter becomes smaller.

Figure 7.14 presents the ratio of pile response computed using silt p-y curves to

the pile response obtained by using the proposed p-y curves. Again, as the pile diameter

increases, the agreement of computed responses between silt p-y curves and proposed p-y

curves improves for the range of pile diameters tested. Additional analyses on larger pile

266

diameters than those tested again indicate that using silt p-y curves overestimates the pile

response.

7.2.3 Comparison of Capability of Various p-y Curves

In this section, the ratio of pile head displacement, maximum moment, and depth

to maximum moment based on different p-y curves is compared to evaluate which of the

existing p-y curves are the most appropriate to predict the response in weakly cemented

sand. Figures 7.15 to 7.18 show that the cemented sand p-y curves proposed by Ismael

(1990) are the most accurate in predicting the pile response in weakly cemented sand for

all diameters tested; whereas, Reese’s sand p-y curves are the most conservative p-y

curves for the range of pile diameters tested. Silt p-y curves are the second best in

predicting pile response. The difference in the pile response is noticeably observed for

the 0.4-m pile and it becomes less significant for the 1.2-m pile.

It is noted that none of the existing p-y curves considered in this study can model

the pile response accurately for a wide range of pile diameters. In addition, it appears to

be non-conservative if the large diameter piles are implemented as discussed in the earlier

section. These p-y curves should therefore be used with caution when analyzing the

lateral response of large diameter piles (more than 1.2 m).

For pile diameter less than 1.2 m, using sand p-y curves proposed by Reese et al.

(1974) yields the lower bound for estimating the load-displacement curves, as well as the

maximum moment, while the proposed p-y curves gives the upper bound values. In case

of the pile diameter larger than 1.2 m, the API sand p-y curves provide the upper bound

values in estimating the pile response, while the proposed p-y curves yield the lower

bound values.

267

7.3 Summary

The capability in using existing p-y curves to predict the response of pile in

weakly cemented sand for a wide range of pile diameters was evaluated by comparing the

computed response to the measured response from the full-scale lateral testing. Four

different types of p-y curves were considered in this study (i.e., sand p-y curves, Reese et

al. 1974 and API 1987; cemented sand p-y curves, Ismael 1987; silt p-y curves, Reese

and Van Impe 2001). Implementation of the sand p-y curves to predict the response of

piles in weakly cemented sand is generally believed to be a conservative method because

the resistance from the soil cohesion component is neglected. However, the analysis

results showed that using the sand p-y curves is not conservative when analyzes the

response of large diameter piles. The cemented sand p-y curves proposed by Ismale

appear to be the most accurate in predicting the response of pile in weakly cemented sand.

However, none of the p-y curves considered in this study has a capability to accurately

predict the pile response in weakly cemented sand for a wide range of pile diameters.

This is mainly because the pile diameter effect incorporated in all of these p-y curves

appeared to be too much for the weakly cemented soil tested at the site. In fact,

experimental results shows that the pile diameter has insignificant effect on p-y curves

before the soil reached its ultimate soil pressure. Using the existing p-y curves to predict

the pile response in weakly cemented sand should be used with caution, especially for

large diameter piles. If the soil condition considered in design is cemented sand with

the SPT-N values of more than 40, using the proposed p-y curves seems to be more

appropriate, particularly for large diameter piles because it provides a lower bound

estimate of pile response as compared to the use of existing p-y curves. However, if the

cemented sand considered in design has the SPT N-values below 40, the cemented sand

p-y curves proposed by Ismael (1990) may be used by incorporating higher factor of

safety when design for large diameter piles.

268

0 20 40 60y (mm)

0

200

400

600

800

1000

p (k

N/m

)

0 20 40 60y (mm)

0

200

400

600

800

1000

p (k

N/m

)

0.4-m Pile (back-calculated)1.2-m Pile (No.1) (back-calculated)0.4-m Pile (Sand, Reese et. al 1974) 1.2-m Pile (Sand, Reese et. al 1974)0.4-m Pile (Sand, API 1987)1.2-m Pile (Sand, API 1987)

0 20 40 60y (mm)

0

200

400

600

800

1000

p (k

N/m

)

0 20 40 60y (mm)

0

200

400

600

800

1000

p (k

N/m

)

0 20 40 60y (mm)

0

200

400

600

800

1000

p (k

N/m

)


0 20 40 60y (mm)

0

200

400

600

800

1000

p (k

N/m

)



Figure 7.1 Comparison of Back-Calculated p-y Curves with Sand p-y Curves (Reese et al 1974; API 1987) for Depths 0 to 1.5 m

269

0 20 40 60y (mm)

0

400

800

1200

1600

2000

p (k

N/m

)

1.2-m Pile (No.1) (back-calculated)0.4-m Pile (Sand, Reese et. al 1974) 1.2-m Pile (Sand, Reese et. al 1974)0.4-m Pile (Sand, API 1987)1.2-m Pile (Sand, API 1987)

0 20 40 60y (mm)

0

400

800

1200

1600

2000

p (k

N/m

)

0 20 40 60y (mm)

0

400

800

1200

1600

2000

p (k

N/m

)

0 20 40 60y (mm)

0

400

800

1200

1600

2000

p (k

N/m

)

Depth 2.1 m

0 20 40 60y (mm)

0

400

800

1200

1600

2000

p (k

N/m

)


Depth 3.0 mDepth 3.3 m

0 20 40 60y (mm)

0

400

800

1200

1600

2000

p (k

N/m

)

Depth 1.8 m

Figure 7.2 Comparison of Back-Calculated p-y Curves with Sand p-y Curves (Reese et al 1974; API 1987) for Depths 1.8 to 3.3 m

270


0

50

100

150

200Lo

ad (k

N)

MeasuredSand (Reese et al. 1974)Sand (API 1987)

(a) 0.4-m Pile


0

100

200

300

400

Load

(kN

)


0

400

800

1200

Load

(kN

)


0

500

1000

1500

2000

2500

Load

(kN

)

(b) 0.6-m Pile

(c) 0.9-m Pile (d) 1.2-m Pile (No.1)

Figure 7.3 Computed Load-Displacement Curves using Sand p-y Curves (Reese et al 1974; API 1987) Compared to Measured Response (a) 0.4-m Pile, (b) 0.6-m Pile, (c) 0.9-m Pile, and (d) 1.2-m Pile (Pile No.1)

271

010

020

030

0D

ispl

acem

ent (

mm

)

0

2000

4000

6000

8000

Load (kN)

Sand

(API

198

7)Pr

opos

ed p

-y C

urve

s

(a) 1

.8-m

Pile

010

020

030

0D

ispl

acem

ent (

mm

)

0

4000

8000

1200

0

1600

0

Load (kN)

Sand

(API

198

7)Pr

opos

ed p

-y C

urve

s

(b) 2

.4-m

Pile

Figu

re 7

.4

Com

paris

on o

f Lo

ad-D

ispl

acem

ent C

urve

s usi

ng S

and

p-y

Cur

ves (

API

198

7) a

nd P

ropo

sed

p-y

Cur

ves f

or (a

) 1.

8-m

Pile

, (b)

2.4

-m P

ile

272

0.0

1.0

2.0

3.0

4.0

Pile

Hea

d D

ispl

acem

ent R

atio


0

0.5

1

1.5

2

Max

imum

Mom

ent R

atio

0 0.2 0.4 0.6 0.8 1Pile Head Load/Yield Pile Head Load

0

0.5

1

1.5

2

Dep

th to

Max

imum

Mom

ent R

atio

(a)

(b)

(c)

Sand (Reese et al. 1974)

Figure 7.5 Predicted Pile Head Displacement, Maximum Moment, and Depth to Maximum Moment Using Sand p-y Curves (Reese et al. 1974) Compared to Response Obtained Using Back-Calculated p-y Curves for Different Pile Diameters (a) Pile Head Displacement, (b) Maximum Moment, and (c) Depth to Maximum Moment

273

0.0

1.0

2.0

3.0

4.0Pi

le H

ead

Dis

plac

emen

t Rat

io0.4-m Pile0.6-m Pile0.9-m Pile1.2-m Pile1.8-m Pile2.4-m Pile

0

0.5

1

1.5

2

Max

imum

Mom

ent R

atio


0

0.5

1

1.5

2

Dep

th to

Max

imum

Mom

ent R

atio

(a)

(b)

(c)

Sand(API 1987)

Figure 7.6 Predicted Pile Head Displacement, Maximum Moment, and Depth to Maximum Moment Using Sand p-y Curves (API 1987) Compared to Response Obtained Using Back-Calculated p-y Curves for Different Pile Diameters (a) Pile Head Displacement, (b) Maximum Moment, and (c) Depth to Maximum Moment

274

0 20 40 60 80y (mm)

0

200

400

600

800

1000

p (k

N/m

)

0 20 40 60 80y (mm)

0

200

400

600

800

1000

p (k

N/m

)

0.4-m Pile (back-calculated)1.2-m Pile (No.1) (back-calculated)0.4-m Pile (Cemented Sand, Ismael 1990) 1.2-m Pile (Cemented Sand, Ismael 1990)

0 20 40 60 80y (mm)

0

200

400

600

800

1000

p (k

N/m

)

0 20 40 60 80y (mm)

0

200

400

600

800

1000

p (k

N/m

)

0 20 40 60 80y (mm)

0

200

400

600

800

1000

p (k

N/m

)


0 20 40 60 80y (mm)

0

200

400

600

800

1000

p (k

N/m

)



Figure 7.7 Comparison of Back-Calculated p-y Curves with Cemented Sand p-y Curves (Ismael 1990) for Depths 0 to 1.5 m

275

0 20 40 60 80y (mm)

0

400

800

1200

1600

2000

p (k

N/m

)

1.2-m Pile (No.1) (back-calculated)0.4-m Pile (Cemented Sand, Ismael 1990) 1.2-m Pile (Cemented Sand, Ismael 1990)

0 20 40 60 80y (mm)

0

400

800

1200

1600

2000

p (k

N/m

)

0 20 40 60 80y (mm)

0

400

800

1200

1600

2000

p (k

N/m

)

0 20 40 60 80y (mm)

0

400

800

1200

1600

2000

p (k

N/m

)

Depth 2.1 m

0 20 40 60 80y (mm)

0

400

800

1200

1600

2000

p (k

N/m

)



0 20 40 60 80y (mm)

0

400

800

1200

1600

2000

p (k

N/m

)

Depth 1.8 m

Figure 7.8 Comparison of Back-Calculated p-y Curves with Cemented Sand p-y Curves (Ismael 1990) for Depths 1.8 to 3.3 m

276


0

50

100

150

200Lo

ad (k

N)

MeasuredCemented Sand (Ismale 1990)

(a) 0.4-m Pile


0

100

200

300

400

Load

(kN

)


0

400

800

1200

Load

(kN

)


0

500

1000

1500

2000

2500

Load

(kN

)

(b) 0.6-m Pile

(c) 0.9-m Pile (d) 1.2-m Pile (No.1)

Figure 7.9 Computed Load-Displacement Curves using Cemented Sand p-y Curves (Ismael 1990) Compared to Measured Response (a) 0.4-m Pile, (b) 0.6-m Pile, (c) 0.9-m Pile, and (d) 1.2-m Pile (Pile No.1)

277

0.0

1.0

2.0

3.0

4.0Pi

le H

ead

Dis

plac

emen

t Rat


0

0.5

1

1.5

2

Max

imum

Mom

ent R

atio


0

0.5

1

1.5

2

Dep

th to

Max

imum

Mom

ent R

atio

(a)

(b)

(c)

Cemented Sand (Ismael 1990)

Figure 7.10 Predicted Pile Head Displacement, Maximum Moment, and Depth to Maximum Moment Using Cemented Sand p-y Curves (Ismael 1990) Compared to Response Obtained Using Back-Calculated p-y Curves for Different Pile Diameters (a) Pile Head Displacement, (b) Maximum Moment, and (c) Depth to Maximum Moment

278

0 20 40 60 80y (mm)

0

200

400

600

800

1000

p (k

N/m

)

0 20 40 60 80y (mm)

0

200

400

600

800

1000

p (k

N/m

)

0.4-m Pile (back-calculated)1.2-m Pile (No.1) (back-calculated)0.4-m Pile (SIlt, Reese and Van Impe 2001) 1.2-m Pile (Silt, Reese and Van Impe 2001)

0 20 40 60 80y (mm)

0

200

400

600

800

1000

p (k

N/m

)

0 20 40 60 80y (mm)

0

200

400

600

800

1000

p (k

N/m

)

0 20 40 60 80y (mm)

0

200

400

600

800

1000

p (k

N/m

)


0 20 40 60 80y (mm)

0

200

400

600

800

1000

p (k

N/m

)



Figure 7.11 Comparison of Back-Calculated p-y Curves with Silt p-y Curves (Reese and Van Impe 2001) for Depths 0 to 1.5 m

279

0 20 40 60 80y (mm)

0

1000

2000

3000

p (k

N/m

)

1.2-m Pile (No.1) (back-calculated)0.4-m Pile (Silt, Reese and Van Impe 2001) 1.2-m Pile (Silt, Reese and Van Impe 2001)

0 20 40 60 80y (mm)

0

1000

2000

3000

p (k

N/m

)

0 20 40 60 80y (mm)

0

1000

2000

3000

p (k

N/m

)

0 20 40 60 80y (mm)

0

1000

2000

3000

p (k

N/m

)

Depth 2.1 m

0 20 40 60 80y (mm)

0

1000

2000

3000

p (k

N/m

)


Depth 3.0 mDepth 3.3 m

0 20 40 60 80y (mm)

0

1000

2000

3000

p (k

N/m

)

Depth 1.8 m

Figure 7.12 Comparison of Back-Calculated p-y Curves with Silt p-y Curves (Reese and Van Impe 2001) for Depths 1.8 to 3.3 m

280


0

50

100

150

200Lo

ad (k

N)

MeasuredSilt (Reese and Van Impe 2001)

(a) 0.4-m Pile


0

100

200

300

400

Load

(kN

)


0

400

800

1200

Load

(kN

)


0

500

1000

1500

2000

2500

Load

(kN

)

(b) 0.6-m Pile

(c) 0.9-m Pile (d) 1.2-m Pile (No.1)

Figure 7.13 Computed Load-Displacement Curves using Silt p-y Curves (Reese and Van Impe 2001) Compared to Measured Response (a) 0.4-m Pile, (b) 0.6-m Pile, (c) 0.9-m Pile, and (d) 1.2-m Pile (Pile No.1)

281

0.0

1.0

2.0

3.0

4.0Pi

le H

ead

Dis

plac

emen

t Rat


0

0.5

1

1.5

2

Max

imum

Mom

ent R

atio


0

0.5

1

1.5

2

Dep

th to

Max

imum

Mom

ent R

atio

(a)

(b)

(c)

Silt (Reese and Van Impe 2001)

Figure 7.14 Predicted Pile Head Displacement, Maximum Moment, and Depth to Maximum Moment Using Silt p-y Curves (Reese and Van Impe 2001) Compared to Response Obtained Using Back-Calculated p-y Curves for Different Pile Diameters (a) Pile Head Displacement, (b) Maximum Moment, and (c) Depth to Maximum Moment

282

0.0

1.0

2.0

3.0

4.0Pi

le H

ead

Dis

plac

emen

t Rat

io

Sand (Reese et al. 1974)Sand (API 1987)Cemented Sand (Ismael 1990)Silt (Reese and Van Impe 2001)

0

0.5

1

1.5

2

Max

imum

Mom

ent R

atio


0

0.5

1

1.5

2

Dep

th to

Max

imum

Mom

ent R

atio

(a)

(b)

(c)

0.4-m Pile

Figure 7.15 Predicted Pile Head Displacement, Maximum Moment, and Depth to Maximum Moment Using Existing p-y Curves Compared to Response Obtained Using Back-Calculated p-y Curves for 0.4-m Pile (a) Pile Head Displacement, (b) Maximum Moment, and (c) Depth to Maximum Moment

283

0.0

1.0

2.0

3.0

4.0Pi

le H

ead

Dis

plac

emen

t Rat

io


0

0.5

1

1.5

2

Max

imum

Mom

ent R

atio


0

0.5

1

1.5

2

Dep

th to

Max

imum

Mom

ent R

atio

(a)

(b)

(c)

0.6-m Pile


284

0.0

1.0

2.0

3.0

4.0Pi

le H

ead

Dis

plac

emen

t Rat

io


0

0.5

1

1.5

2

Max

imum

Mom

ent R

atio


0

0.5

1

1.5

2

Dep

th to

Max

imum

Mom

ent R

atio

(a)

(b)

(c)

0.9-m Pile


285

0.0

1.0

2.0

3.0

4.0Pi

le H

ead

Dis

plac

emen

t Rat

io


0

0.5

1

1.5

2

Max

imum

Mom

ent R

atio


0

0.5

1

1.5

2

Dep

th to

Max

imum

Mom

ent R

atio

(a)

(b)

(c)

1.2-m Pile


286


287

Chapter 8 SUMMARY AND CONCLUSIONS

8.1 Summary

The effect of pile diameter on modulus of subgrade reaction (i.e., the stiffness of

the p-y curves) was investigated in this study. The study included the analytical study on

the effect of pile diameter on the pile response in homogeneous soil using 3-D finite

element analyses with both linear and nonlinear soil models. This was followed by the

evaluation of pile diameter effect using the results from the full-scale lateral pile load

tests. Cast-In-Drilled-Holes (CIDH) piles with various diameters ranging from 0.4 m to

1.2 m were installed in dense weakly cemented sand and tested under both vibration and

lateral load testing. The results of vibration tests were utilized to evaluate the effect of

pile diameter on the initial modulus of subgrade reaction, while the results from static

lateral load tests were used to back-calculate the p-y curves. The back-calculated p-y

curves for each pile diameter were then compared to evaluate the pile diameter effect at

larger displacement levels. In addition to the study of pile diameter effect, the

enhancement of seismic performance of CIDH piles due to the effect of external

confinement from the soil was evaluated using cyclic lateral load tests.

8.2 Conclusions

The main findings of this research study on the effect of pile diameter on the p-y

curves based on both experimental and analytical results are provided as the followings:

• The results from 3-D finite element analysis using linear soil model showed

that the pile diameter has some effect on the modulus of the subgrade reaction,

but this effect appears to be insignificant, particularly when taking into

account the effect of increasing of pile stiffness with the pile diameter.

288

Furthermore, soil nonlinearity tends to increase the pile diameter effect on the

pile response.

• The analyses based on vibration test results showed that pile diameter has very

small effect on initial modulus of subgrade reaction.

• Based on the back-calculated p-y curves of various pile diameters, it was

found that the pile diameter has insignificant effect on the p-y curves at the

displacement level below the ultimate soil resistance. Beyond this range, the

ultimate soil resistance increases as the pile diameter increases.

• Using the standard p-y curves currently available in the literature

underestimates the soil resistance in weakly cemented sand for small diameter

piles, but tends to overestimate the soil resistance to large diameter piles.

Therefore, the use of these standard p-y curves for large diameter piles in

weakly cemented sand should be used with caution.

• The proposed methodology for developing p-y curves for weakly cemented

sand are simple and appears to be appropriate to use for cemented sand along

the coast of Southern California with the SPT N-values of above 40.

• Results from the cyclic lateral pile load tests showed that only moderate level

of transverse reinforcement (0.6%) can provide adequate seismic performance

with the displacement ductility of more than 5 because the external

confinement from the soil considerably enhances inelastic behavior of CIDH

piles. The confinement effect of the soil at the test site was estimated to be

equivalent to the additional amount of transverse reinforcement of 0.7%

• The results from lateral load tests show that the depth of plastic hinge ranges

from 1.5D for the 0.4-m pile to 2.5D for the 1.2-m pile, which is in the range

of typical values assumed in design (Budek 1997). The magnitude of moment

becomes negligible at depth below 6D for all pile diameters tested.

289

APPENDIX A

290

Location : East CampusBorehole : BH-1Sample No : S-1Depth : 1.52-1.98 m

Sieve Sieve PassingNo. Size %

(mm) # 10 2.000 97.4 # 30 0.600 96.6 # 40 0.425 89.6 # 60 0.250 59.9 # 100 0.150 37.0 # 120 0.125 31.2 # 170 0.090 25.6 # 200 0.075 23.8

USCS SM



(mm) # 10 2.000 98.4 # 30 0.600 97.9 # 40 0.425 93.2 # 60 0.250 64.7 # 100 0.150 39.2 # 120 0.125 32.8 # 170 0.090 27.0 # 200 0.075 25.7

USCS SM



(mm) # 10 2.000 99.5 # 30 0.600 98.8 # 40 0.425 94.9 # 60 0.250 75.0 # 100 0.150 54.4 # 120 0.125 48.0 # 170 0.090 41.7 # 200 0.075 40.0

USCS SC

Grain Size Distribution

0

10

20

30

40

50

60

70

80

90

100

0.010.1110Diameter Size (mm)

Perc

ent P

assi

ng (%

)

Sand Silt+ClayGravel

0

10

20

30

40

50

60

70

80

90

100

0.010.1110 Diameter Size (mm)

Perc

ent P

assi

ng (%

)


0

10

20

30

40

50

60

70

80

90

100


Perc

ent P

assi

ng (%

)


Figure A-1 Results of Gradation Analysis (Borehole BH-1)

291



(mm) # 10 2.000 99.7 # 30 0.600 99.0 # 40 0.425 94.7 # 60 0.250 74.6 # 100 0.150 53.2 # 120 0.125 46.8 # 170 0.090 40.1 # 200 0.075 38.1

USCS SM



(mm) # 10 2.000 99.0 # 30 0.600 92.2 # 40 0.425 71.1 # 60 0.250 42.8 # 100 0.150 27.1 # 120 0.125 22.4 # 170 0.090 17.8 # 200 0.075 16.1

USCS SM



(mm) # 10 2.000 97.9 # 30 0.600 90.0 # 40 0.425 66.0 # 60 0.250 37.4 # 100 0.150 24.9 # 120 0.125 21.2 # 170 0.090 16.9 # 200 0.075 15.4

USCS SC


0

10

20

30

40

50

60

70

80

90

100


Perc

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Figure A-2 Results of Gradation Analysis (Borehole BH-1, Continued)

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(mm) # 10 2.000 99.5 # 30 0.600 95.8 # 40 0.425 80.5 # 60 0.250 54.2 # 100 0.150 40.3 # 120 0.125 36.2 # 170 0.090 31.5 # 200 0.075 29.6

USCS SC



(mm) # 10 2.000 96.8 # 30 0.600 90.6 # 40 0.425 69.0 # 60 0.250 40.7 # 100 0.150 27.3 # 120 0.125 23.3 # 170 0.090 19.1 # 200 0.075 17.9

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(mm) # 10 2.000 95.9 # 30 0.600 90.6 # 40 0.425 75.9 # 60 0.250 56.1 # 100 0.150 45.1 # 120 0.125 41.5 # 170 0.090 36.9 # 200 0.075 35.3

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Location : East CampusBorehole : BH-1Sample No : S-11 (Bottom)Depth : 16.76-17.22 m


(mm) # 10 2.000 93.7 # 30 0.600 89.2 # 40 0.425 69.3 # 60 0.250 39.2 # 100 0.150 25.3 # 120 0.125 21.6 # 170 0.090 17.1 # 200 0.075 15.3

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Location : East CampusBorehole : BH-1Sample No : S-12 (Top)Depth : 19.81-20.27 m


(mm) # 10 2.000 98.8 # 30 0.600 94.1 # 40 0.425 77.8 # 60 0.250 55.5 # 100 0.150 45.5 # 120 0.125 42.6 # 170 0.090 39.1 # 200 0.075 37.3

USCS SM



(mm) # 10 2.000 99.5 # 30 0.600 96.3 # 40 0.425 84.6 # 60 0.250 64.6 # 100 0.150 51.9 # 120 0.125 47.6 # 170 0.090 41.4 # 200 0.075 38.4

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(mm) # 10 2.000 97.9 # 30 0.600 96.8 # 40 0.425 92.3 # 60 0.250 72.7 # 100 0.150 57.2 # 120 0.125 53.2 # 170 0.090 48.5 # 200 0.075 46.5

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(mm) # 10 2.000 99.4 # 30 0.600 97.2 # 40 0.425 89.1 # 60 0.250 62.0 # 100 0.150 37.6 # 120 0.125 30.9 # 170 0.090 24.9 # 200 0.075 23.0

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(mm) # 10 2.000 99.0 # 30 0.600 90.0 # 40 0.425 68.4 # 60 0.250 42.4 # 100 0.150 28.3 # 120 0.125 24.0 # 170 0.090 19.6 # 200 0.075 18.3

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Figure A-5 Results of Gradation Analysis (Borehole BH-2)

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(mm) # 10 2.000 97.6 # 30 0.600 87.2 # 40 0.425 65.5 # 60 0.250 39.9 # 100 0.150 25.5 # 120 0.125 21.2 # 170 0.090 16.9 # 200 0.075 15.5

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(mm) # 10 2.000 98.1 # 30 0.600 91.3 # 40 0.425 70.7 # 60 0.250 43.5 # 100 0.150 29.2 # 120 0.125 25.1 # 170 0.090 20.6 # 200 0.075 18.8

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(mm) # 10 2.000 94.3 # 30 0.600 87.5 # 40 0.425 68.5 # 60 0.250 43.4 # 100 0.150 31.0 # 120 0.125 27.3 # 170 0.090 23.1 # 200 0.075 21.5

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(mm) # 10 2.000 98.0 # 30 0.600 94.2 # 40 0.425 90.1 # 60 0.250 83.6 # 100 0.150 77.3 # 120 0.125 74.2 # 170 0.090 68.5 # 200 0.075 65.4

USCS ML



(mm) # 10 2.000 84.8 # 30 0.600 83.6 # 40 0.425 81.7 # 60 0.250 77.5 # 100 0.150 74.0 # 120 0.125 72.7 # 170 0.090 70.1 # 200 0.075 68.2

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Location : East CampusBorehole : BH-2Sample No : S-10 (Middle)Depth : 15.24-15.70 m


(mm) # 10 2.000 91.6 # 30 0.600 87.3 # 40 0.425 72.1 # 60 0.250 48.4 # 100 0.150 35.9 # 120 0.125 32.0 # 170 0.090 26.9 # 200 0.075 25.0

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(mm) # 10 2.000 96.9 # 30 0.600 96.3 # 40 0.425 95.4 # 60 0.250 93.7 # 100 0.150 92.0 # 120 0.125 91.2 # 170 0.090 88.5 # 200 0.075 85.7

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(mm) # 10 2.000 90.8 # 30 0.600 89.5 # 40 0.425 88.2 # 60 0.250 86.5 # 100 0.150 84.9 # 120 0.125 84.3 # 170 0.090 82.9 # 200 0.075 81.5

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(mm) # 10 2.000 86.8 # 30 0.600 84.0 # 40 0.425 75.0 # 60 0.250 60.9 # 100 0.150 50.9 # 120 0.125 47.5 # 170 0.090 43.2 # 200 0.075 40.9

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(mm) # 10 2.000 97.3 # 30 0.600 96.2 # 40 0.425 90.3 # 60 0.250 67.9 # 100 0.150 41.7 # 120 0.125 33.2 # 170 0.090 26.0 # 200 0.075 22.8

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(mm) # 10 2.000 98.4 # 30 0.600 97.3 # 40 0.425 93.7 # 60 0.250 87.4 # 100 0.150 81.8 # 120 0.125 79.2 # 170 0.090 74.0 # 200 0.075 71.3

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APPENDIX B

301

Table B.1 Summary of Soil Properties at Charter School Site

Sample No. Depth (m) Dry Density

(kN/m3) Moisture

Content (%) Cohesion (kN/m2)

Angle of Friction

(Degree)

Penetration Resistance (Blows/ft)

SB 1-3 0.61 16.8 17.5 50/8" SB 1-5 1.22 16.9 14.6 50/8" SB 1-6 2.74 17.1 14.2 50/6" SB 1-7 4.27 50/5" SB 1-8 5.79 16.8 19.0 50/5" SB 1-9 7.32 50/6" SB 1-10 8.84 50/5" SB 1-11 10.36 16.5 20.6 50/4" SB 2-3 1.22 17.9 9.8 50/4" SB 2-5 2.74 50/4" SB 2-6 4.27 18.0 9.7 50/5" SB 2-7 5.79 50/4" SB 2-8 7.32 15.8 8.5 50/4" SB 3-3 1.22 50/5" SB 3-4 2.74 17.9 9.5 50/5" SB 3-5 4.27 50/6" SB 3-6 5.79 17.3 8.9 50/4" SB 4-1 1.22 17.2 8.8 -- SB 5-1 0.61 19.0 10.0 50/4" SB 5-2 4.27 16.7 18.6 50/5" SB 5-3 5.79 50/5" SB 5-4 7.32 16.2 18.5 50/4" SB 6-1 1.22 18.1 9.9 40.7 31 -- SB 6-2 2.74 17.6 10.8 52.7 30 50/4" SB 6-3 4.27 50/5" SB 6-4 5.79 18.4 12.7 50/6" SB 6-5 7.32 50/6" SB 7-1 0.61 18.5 11.0 50/7" SB 7-3 1.22 18.3 8.3 50/3" SB 7-4 2.74 50/4" SB 7-5 4.27 50/4" SB 7-6 5.79 16.7 18.6 50/4" SB 7-7 7.32 50/4" SB 7-8 8.84 17.7 17.1 50/4" SB 7-9 10.36 50/3" SB 7-10 11.89 15.9 9.1 50/2.5" SB 8-1 1.52 19.1 7.2 50/5" SB 8-2 3.05 50/3" SB 8-3 4.57 16.7 8.6 50/4" SB 8-4 6.10 50/4" SB 8-5 7.62 50/3" SB 9-2 0.61 19.2 10.0 50/7" SB 9-4 1.52 18.3 7.9 50/4" SB 9-6 3.05 50/4" SB 9-7 4.57 16.6 8.8 50/4" SB 9-8 6.10 50/4" SB 9-9 7.62 15.9 7.5 50/3" SB 10-1 1.52 17.8 12.0 50/5.5" SB 10-2 3.05 50/4" SB 10-3 4.57 17.2 9.3 50/4" SB 10-4 6.10 50/4" SB 11-3 1.52 50/3.5" SB 11-4 3.05 50/4" SB 11-5 4.57 50/4" SB 11-6 6.10 50/4"

Note: Extracted from GEOCON (1998). Geotechnical Investigation–Charter School Site, University of California, San Diego, August 1998.

302

Table B.2 Summary of Soil Properties at East Campus Utilities Plant Test Site

Sample No. Depth (m)

Dry Density (kN/m3)

Moisture Content (%)

Cohesion (kN/m2)

Angle of Friction

(Degree)


1-3 1.52 17.0 6.6 50/3" 1-4 1.83 17.8 10.6 33.5 32 -- 1-5 3.05 18.7 7.2 50/5" 1-7 4.57 14.6 11.6 50/5" 1-8 6.10 15.4 8.0 50/5" 1-9 7.62 50/6" 1-11 9.14 16.2 7.4 50/6" 3-1 0.00 16.9 5.5 50/3" 3-3 1.52 17.7 6.0 50/5" 3-5 3.05 16.7 9.3 78/10" 3-7 4.57 16.5 8.3 89/10" 3-8 6.10 50/5" 4-1 0.00 17.0 6.0 14.4 32 70 4-3 2.13 14.1 8.4 81/10" 4-5 3.05 15.4 6.6 50/6" 4-7 4.57 15.3 7.7 50/6" 4-8 6.10 50/6" 5-1 0.00 18.0 5.4 72/11" 5-3 2.13 88/9" 5-4 3.05 18.5 7.9 95/9" 5-6 4.57 16.9 -- 50/6" 5-7 6.10 50/5"

Note: Extracted from GEOCON (2000). Geotechnical Investigation–UCSD East Campus Utilities Plant, University of California, November 2000.

303

APPENDIX C

304

Table C.1 Summary of Soil Properties at UCSD Cancer Center Building Project


Dry Density (kN/m3)


Cohesion (kN/m2)

Angle of Friction

(Degree)


B1-5 3.05 91/9" B1-7 4.57 50/5" B1-8 6.10 15.3 15.3 50/5" B1-10 9.14 15.6 15.7 50/5" B1-11 10.67 13.0 6.2 50/5" B1-12 12.19 50/5" B1-13 13.72 17.3 17.3 50/5" B1-14 15.24 17.6 9.5 35.9 34 50/3" B2-6 4.57 50/5" B2-8 6.10 50/4" B2-9 7.62 17.8 16.6 50/4" B2-10 9.14 16.6 15.7 52.7 33 50/6" B2-11 10.67 17.0 18.1 50/4" B2-13 12.19 16.4 21.3 88/7" B2-15 13.72 50/4" B2-16 15.24 19.2 12.6 50/2" B3-2 1.52 50/6" B3-3 3.05 77/9" B3-4 4.57 77/8" B3-6 6.10 15.7 15.7 50/6" B3-7 7.62 16.6 20.1 50/6" B3-9 9.14 75/10" B3-11 10.67 14.9 13.4 50/6" B3-12 12.19 16.5 17.6 50/6" B3-13 13.72 17.5 7.5 50/6" B3-15 15.24 50/4" B4-2 1.52 73 B4-4 3.05 50/4" B4-6 4.57 64 B4-7 6.10 17.3 19.9 50/5" B4-9 7.62 50/6" B4-10 9.14 50/6" B4-11 10.67 15.6 8.9 50/5" B4-12 12.19 15.7 7.9 50/5" B4-13 13.72 50/6" B4-14 15.24 17.0 17.3 50/6"

Note: Extracted from GEOCON (2000). Geotechnical Investigation–UCSD Cancer Center Building Project No. 3245, University of California, San Diego, October 2000.

305

Table C.1 Summary of Soil Properties at UCSD Cancer Center Building Project (Cont’d)


Dry Density (kN/m3)


Cohesion (kN/m2)

Angle of Friction

(Degree)


B5-3 3.05 68 B5-5 4.57 17.4 15.5 50/4" B5-6 6.10 17.1 19 84/7" B5-7 7.62 50/4" B5-9 9.14 16.1 20 82/9" B5-10 10.67 14.6 7.9 50/4 B5-11 12.19 50/5 B5-12 13.72 16.5 19.3 82/8" B5-13 15.24 50/5" B6-3 3.05 50/6" B6-4 4.57 50/4" B6-6 6.10 16.5 8.9 50/4" B6-7 7.62 15.9 10.9 50/3" B6-8 9.14 17.1 19.2 96/10" B6-10 10.67 17.1 11.8 50/4" B6-11 12.19 14.9 9.3 50/4" B7-3 4.57 50/6" B7-5 6.10 16.0 9.1 50/6" B7-6 7.62 16.2 8.4 50/6" B7-7 9.14 50/6" B7-8 10.67 14.1 28.1 80/10" B7-9 12.19 16.9 17.8 50/5" B8-2 1.52 50/5" B8-3 3.05 50/5" B8-4 4.57 75/9" B8-5 6.10 16.2 7.9 50/6" B8-6 7.62 16.2 7.7 50/6" B8-7 9.14 50/3" B8-9 10.67 16.2 21.5 50/4"

Note: Extracted from GEOCON (2000). Geotechnical Investigation–UCSD Cancer Center Building Project No. 3245, University of California, San Diego, October 2000.

306

Table C.2 Summary of Soil Properties at UCSD EBU 3 and EBU 4 Site


Dry Density (kN/m3)


Cohesion (kN/m2)

Angle of Friction

(Degree)


B1-3 3.05 16.5 17.9 50.3 33 91 B1-4 4.57 16.3 16.8 98 B1-5 6.10 16.8 20.0 100 B2-2 3.05 15.3 20.8 87 B2-3 4.57 15.7 19.3 100 B2-4 6.10 16.1 20.9 40.7 20 89 B2-5 7.62 17.2 17.3 100 B2-6 9.14 100 B3-2 3.05 16.1 18.0 100 B3-3 4.57 15.4 13.1 100 B3-4 6.10 15.2 15.1 100 B4-3 3.05 17.1 19.6 89 B4-4 4.57 16.0 19.0 87 B4-5 6.10 88 B4-6 7.62 16.9 18.2 80 B4-7 9.14 16.8 19.8 100 B5-3 3.05 16.1 21.3 100 B5-4 4.57 17.3 19.5 89 B5-5 12.19 16.0 18.6 100

Note: Extracted from GEOCON (2000). Geotechnical Investigation–UCSD EBU 3A, 4A, 3B and 4B, University of California, San Diego, November 2000.

307

Table C.3 Summary of Soil Properties at Gilman Drive Parking Structure Site


Dry Density (kN/m3)


Cohesion (kN/m2)

Angle of Friction

(Degree)


B1-1 0.61 18.0 14.4 27 B1-2 1.52 15.1 23.8 37 B1-4 3.05 16.6 22.8 42 B1-5 4.57 16.2 21.4 52 B1-6 6.10 16.2 21.4 52/6" B1-7 7.62 16.4 20.3 58/6" B1-8 9.14 58/6" B3-3 1.52 17.6 12.4 54 B3-4 3.05 17.2 11.2 73 B3-6 6.10 17.3 7.7 65/6" B3-8 9.14 60/6" B3-9 12.19 50/6" B4-3 1.52 17.5 9.7 39 B4-5 3.05 17.4 11.5 97/10" B4-7 6.10 53/6"

Note: Extracted from GEOCON (1998). Geotechnical Investigation–Gilman Drive Parking Structure, University of California, San Diego, September 1998.

308

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